existence of solutions to a model for sparse one dimensional fluids abstract we prove the global existence of solutions to a model for a viscous compressible barotropic fluid initially occupying a general open subset of a finite one dimensional interval the fluid equations are applied only on the support of the density understood in the sense of distributions this support must be tracked and accommodation must be made for the possibly infinite number of collisions of fluid packets occurring on a possibly dense set of collision times our approach avoids certain nonphysical properties of solutions which are constructed as limits of solutions in which artificial mass has been inserted

approximations of two dimensional mean field games with nonsymmetric controls abstract the numerical methods are presented for solving economic problems formulated in the mean field game mfg form the mean field equilibrium is a solution of the coupled system of two parabolic partial differential equations the fokker planck kolmogorov equation and the hamilton jacobi bellman one the description focuses on the discrete approximation of these equations and on the application of the mfg theory directly at discrete level this approach results in an efficient algorithm for finding the corresponding grid control functions contrary to other difference schemes here the semi lagrangian approximation is applied which improves properties of a discrete problem of this type this implies the fast convergence of an iterative algorithm for the minimization of the cost functional the constructed algorithms are implemented to the problem of carbon dioxide pollution

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

on the well posedness of the full compressible navier stokes system in critical besov spaces abstract we are concerned with the cauchy problem of the full compressible navier stokes equations satisfied by viscous and heat conducting fluids in r n we focus on the so called critical besov regularity framework in this setting it is natural to consider initial densities 0 velocity fields u 0 and temperatures 0 with a 0 0 1 b p 1 n p u 0 b p 1 n p 1 and 0 b p 1 n p 2 after recasting the whole system in lagrangian coordinates and working with the total energy along the flow rather than with the temperature we discover that the system may be solved by means of banach fixed point theorem in a critical functional framework whenever the space dimension is n 2 and 1 p 2 n back to eulerian coordinates this allows to improve the range of p s for which the system is locally well posed compared to 7

the relations of go and stop wave to car accidents in a cellular automaton with velocity dependent randomization abstract in this paper we numerically study the probability p ac of the occurrence of traffic accidents in the nagel schreckenberg ns model with velocity dependent randomization vdr numerical results show that there is a critical density over which car accidents occur but below which no car accidents happen different from the accident probability in the ns model the accident probability in the vdr model monotonously decreases with increase of car density above the critical density the value of the accident probability is only determined by the stochastic noise and the number of cars on road in the stochastic vdr model with the speed limit v max 1 no critical density exists and car accidents happen in the whole density region the braking probabilities of standing cars and moving cars have different influences on the accident probability a mean field theory reveals that the accident probability is proportional to the mean density of go and stop wave per time step theoretical analyses give excellent agreement with numerical results in the vdr model

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

global existence and optimal decay rates for the timoshenko system the case of equal wave speeds abstract we first show the global existence and optimal decay rates of solutions to the classical timoshenko system in the framework of besov spaces due to the non symmetric dissipation the general theory for dissipative hyperbolic systems see 31 cannot be applied to the timoshenko system directly in the case of equal wave speeds we construct global solutions to the cauchy problem pertaining to data in the spatially besov spaces furthermore the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis consequently the optimal decay estimates of solution and its derivatives of fractional order are shown by time weighted energy approaches in terms of low frequency and high frequency decompositions as a by product the usual decay estimate of l 1 r l 2 r type is also shown

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

numerical investigation of cavitation in multidimensional compressible flows the compressible navier stokes equations for an ideal polytropic gas are considered in r n n 2 3 the question of possible vacuum formation an open theoretical problem is investigated numerically using highly accurate computational methods the flow is assumed to be symmetric about the origin with a purely radial velocity field the numerical results indicate that there are weak solutions to the navier stokes system in two and three space dimensions which display formation of vacuum when the initial data are discontinuous and sufficiently large the initial density is constant while the initial velocity field is symmetric points radially away from the origin and belongs to h s loc for all s n 2 in addition in the one dimensional case the numerical solutions are in agreement with known theoretical results

boussinesq system with measure forcing the paper analyzes the navier stokes system coupled with the convective diffusion equation responsible for thermal effects it is a version of the boussinesq approximation with a heat source the problem is studied in the two dimensional plane and the heat source is a measure transported by the flow for arbitrarily large initial data we prove global in time existence of unique regular solutions measure being a heat source limits regularity of constructed solutions and it requires a non standard framework of inhomogeneous besov spaces of the l infty 0 t b s p infty type the uniqueness of solutions is proved by using the lagrangian coordinates

exact stationary state for an asymmetric exclusion process with fully parallel dynamics the exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product ansatz we give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices we prove the stationarity via a cancellation mechanism and by making use of an explicit representation of the matrix algebra we easily find closed expressions for the correlation functions in the general probabilistic case asymptotic expressions obtained by making use of earlier results allow us to derive the exact phase diagram

the large time behavior of solutions in the critical l p framework for compressible viscous and heat conductive gas flows in this paper we are concerned with non isentropic navier stokes equations governing compressible viscous and heat conductive gases we formulate an additional regularity assumption of low frequencies in rd d 3 and then establish the sharp time weighted inequality which allows us to get the time decay estimates of global strong solutions in the lp critical besov spaces precisely it is shown that if the initial data belong to some besov space b2 s1 with s1 1 d2 s0 s0 2dp d2 then the lp norm of the critical global solutions admits the time decay t s12 d2 12 1p in particular t d2p if s1 s0 which coincides with that of the heat kernel in the lp framework in comparison with the work of danchin and xu j math fluid mech 20 1641 1665 2018 the low frequency assumption is improved such that the regularity s1 belongs to the whole range 1 d2 s0

on one dimensional compressible navier stokes equations with degenerate viscosity and constant state at far fields in this paper we are concerned with the cauchy problem for one dimensional compressible isentropic navier stokes equations with density dependent viscosity 0 and pressure p 1 we will establish the global existence and asymptotic behavior of weak solutions for any 0 and 1 under the assumption that the density function keeps a constant state at far fields in particular in the case that 0 12 we obtain the large time behavior of the strong solution obtained by mellet and vasseur when the solution has a lower bound no vacuum

well posedness in critical spaces for incompressible viscoelastic fluid system abstract in this paper we study the well posedness in critical spaces of incompressible viscoelastic fluid system of oldroyd model precisely for this system with initial data in besov space of critical regularity we prove the existence and uniqueness of the local solution which is also shown to exist globally in time provided the initial data is small under certain norms

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

compressible navier stokes system large solutions and incompressible limit abstract here we prove the existence of global in time regular solutions to the two dimensional compressible navier stokes equations supplemented with arbitrary large initial velocity v 0 and almost constant density 0 for large volume bulk viscosity the result is generalized to the higher dimensional case under the additional assumption that the strong solution of the classical incompressible navier stokes equations supplemented with the divergence free projection of v 0 is global the systems are examined in r d with d 2 in the critical b 2 1 s besov spaces framework

a low frequency assumption for optimal time decay estimates to the compressible navier stokes equations the global existence issue in critical spaces for compressible navier stokes equations was addressed by danchin invent math 141 579 614 2000 and then developed by charve and danchin arch rational mech anal 198 233 271 2010 chen et al commun pure appl math 63 1173 1224 2010 and haspot arch rational mech anal 202 427 460 2011 in more general lp setting the main aim of this paper is to exhibit more precisely time decay estimates of solutions constructed in the critical regularity framework to the best of our knowledge the low frequency assumption usually plays a key role in the large time asymptotics of solutions which was firstly observed by matsumura and nishida j math kyoto univ 20 67 104 1980 in the l 1 mathbb r d space we now claim a new low frequency assumption for barotropic compressible navier stokes equations which may be of interest in the mathematical analysis of viscous fluids precisely if the initial density and velocity additionally belong to some besov space dot b sigma 1 2 infty mathbb r d with the regularity sigma 1 in 1 d 2 2d p d 2 then a sharp time weighted inequality including enough time decay information can be available where optimal decay exponents for the high frequencies are exhibited the proof mainly depends on some non standard besov product estimates as a by product those optimal time decay rates of lq lr type are also captured in the critical framework

a sharp time weighted inequality for the compressible navier stokes poisson system in the critical l p framework abstract the compressible navier stokes poisson system takes the form of usual navier stokes equations coupled with the self consistent poisson equation which is used to simulate the transport of charged particles under the electrostatic potential force in this paper we focus on the large time behavior of global strong solutions in the l p critical besov spaces inspired by the dissipative effect arising from poisson potential we formulate a new regularity assumption of low frequencies and then establish the sharp time weighted inequality which leads to the optimal time decay estimates of strong solutions indeed we see that the decay of density is faster at the half rate than that of velocity which is a different ingredient in comparison with the situation of compressible navier stokes equations our proof mainly depends on tricky and non classical besov product estimates with respect to various sobolev embeddings

incompressible limit of oldroyd b fluids in the whole space abstract this paper is dedicated to the study of compressible oldroyd b model in the framework of critical spaces we first prove the local well posedness for the compressible oldroyd b model with initial data 0 1 u 0 0 b 2 1 d 2 b 2 1 d 2 1 d b 2 1 d 2 d d the global well posedness is also established provided the initial data and coupling constant are sufficiently small on the basis of this we also consider the incompressible limit problem for ill prepared initial data we prove that as the mach number tends to zero the global solution to the compressible oldroyd b fluids converges to the solution to the corresponding incompressible model in some function spaces in the meanwhile the converge rates are obtained in some sense to fulfill our proof we give a new commutator estimate

existence of global weak solutions for 3d degenerate compressible navier stokes equations in this paper we prove the existence of global weak solutions for 3d compressible navier stokes equations with degenerate viscosity the method is based on the bresch and desjardins commun math phys 238 211 223 2003 entropy conservation the main contribution of this paper is to derive the mellet and vasseur commun partial differ equ 32 431 452 2007 type inequality for weak solutions even if it is not verified by the first level of approximation this provides existence of global solutions in time for the compressible barotropic navier stokes equations the result holds for any gamma 1 in two dimensional space and for 1 gamma 3 in three dimensional space in both case with large initial data possibly vanishing on the vacuum this solves an open problem proposed by lions mathematical topics in fluid mechanics vol 2 compressible models 1998

the r bounded operator families arising from the study of the barotropic compressible flows with free surface abstract in this paper we study some model problem associated to the free boundary value problem of the barotropic compressible navier stokes equations in general smooth domain with taking surface tension into account to obtain the maximal l p l q regularity property of the model problem we prove the existence of r bounded operator families of the resolvent problem via weis theory on operator valued fourier multipliers

global well posedness of the cauchy problem of two dimensional compressible navier stokes equations in weighted spaces abstract in this paper we study the global well posedness of classical solution to 2d cauchy problem of the compressible navier stokes equations with large initial data and vacuum it is proved that if the shear viscosity is a positive constant and the bulk viscosity is the power function of the density that is with 3 then the 2d cauchy problem of the compressible navier stokes equations on the whole space r 2 admits a unique global classical solution u which may contain vacuums in an open set of r 2 note that the initial data can be arbitrarily large to contain vacuum states various weighted estimates of the density and velocity are obtained in this paper and these self contained estimates reflect the fact that the weighted density and weighted velocity propagate along with the flow

stochastic exclusion processes with extended hopping we study the effects of extended hopping in the stochastic asymmetric simple exclusion process asep of one dimension a modified asep with four parameters is proposed the current and bulk density are calculated two different phases with a curved boundary are observed the phase of maximum current is absent we also present the unusual density fluctuations near both boundaries the characteristic of the stochastic dynamics with extended hopping is pointed out

global well posedness in spatially critical besov space for the boltzmann equation the unique global strong solution in the chemin lerner type space to the cauchy problem on the boltzmann equation for hard potentials is constructed in a perturbation framework such a solution space is of critical regularity with respect to the spatial variable and it can capture the intrinsic properties of the boltzmann equation for the proof of global well posedness we develop some new estimates on the nonlinear collision term through the littlewood paley theory

global strong solutions for equations related to the incompressible viscoelastic fluids with a class of large initial data abstract we investigate the global strong solutions for a system related to the incompressible viscoelastic fluids of oldroyd b type with a class of large initial data e 0 e 0 i j n n v 0 v 01 v 0 n we obtain the global existence and uniqueness of a solution provided that e 0 h v 0 h are sufficiently small in b 2 1 n 2 1 b 2 1 n 2 b 2 1 n 2 1 while e 0 n and v 0 n are large where e 0 h e 0 i j n 1 n v 0 h v 01 v 0 n 1 and e 0 n e 0 n 1 e 0 n n

the cauchy problem for the compressible navier stokes equations in the l p framework the global in time existence of regular solutions to the compressible navier stokes equations in the whole space is obtained the solutions are close to nontrivial equilibrium solutions moreover the result is sharp in the lp framework the velocity of the fluid belongs to wr2 1 and the initial density to w1r with r 3

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

on the existence of local classical solutions to the navier stokes equations with degenerate viscosities in this paper we consider the three dimensional cauchy problem of compressible navier stokes equations with degenerate viscosities depending on density with the initial data containing vacuum at far fields we prove the local existence of regular solutions with some compatibility conditions the regular solution is classical due to the smoothing effect of the velocity u in this paper we consider the three dimensional cauchy problem of compressible navier stokes equations with degenerate viscosities depending on density with the initial data containing vacuum at far fields we prove the local existence of regular solutions with some compatibility conditions the regular solution is classical due to the smoothing effect of the velocity u

existence and uniqueness of small energy weak solution to multi dimensional compressible navier stokes equations with large external potential force we study the 3 d compressible navier stokes equations with an external potential force and a general non decreasing pressure we prove the global in time existence of weak solutions with small energy initial data and with densities being non negative and essentially bounded a solution may have large oscillations and contain vacuum states no smallness assumption is made on the external force nor the initial perturbation in l for density initial velocity u0 is taken to be bounded in lq for some q 6 and no further regularity assumption is imposed on u0 finally we discuss the uniqueness of weak solutions

global well posedness of compressible navier stokes equations for some classes of large initial data we prove the global well posedness of three dimensional compressible navier stokes equations for some classes of large initial data which may have large oscillation for the density and large energy for the velocity the proof uses the special structure of the system especially the effective viscous flux

boundary effects on car accidents in a cellular automaton model in this paper we numerically study the probability pac of occurrence of car accidents in the nagel schreckenberg ns model with open boundary condition in the deterministic ns model numerical results show that there exists a critical value of extinction rate above which no car accidents occur and below which the probability pac is independent of the speed limit vmax and the injection rate but only determined by the extinction rate in the non deterministic ns model the probability pac is a non monotonic function of in the region of low value while it is independent of in the region of high value the stochastic braking not only reduces the occurrence of car accidents but splits degenerate effects of vmax on the probability pac theoretical analyses give an agreement with numerical results in the deterministic ns model and in the non deterministic ns model with vmax 1 in the case of low value region qualitative differences between open and periodic systems in the relations of pac to the bulk density imply that various correlations may exist between the two systems

global strong solutions to radial symmetric compressible navier stokes equations with free boundary in this paper we consider the two dimensional barotropic compressible navier stokes equations with stress free boundary condition imposed on the free surface as the viscosity coefficients satisfies 2 1 we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary in particular we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive and the free boundary propagates along the particle path and expand outwards at an algebraic rate

dangerous situations within the framework of the nagel schreckenberg model this paper investigates the occurrence of dangerous situations ds within the framework of the nagel schreckenberg model the conditions of the ds are modified it is shown that when vmax 1 there will be no ds in both deterministic and non deterministic cases the situation is different for vmax 1 we show that in the deterministic case the probability of ds covers a two dimensional region which depends on both the density and the initial configuration as for the non deterministic case our results are qualitatively the same as previous ones but are quantitatively different

optimal bandwidth selection in nonparametric regression function estimation kernel estimators of an unknown multivariate regression function are investigated a bandwidth selection rule is considered which can be formulated in terms of cross validation under mild assumptions on the kernel and the unknown regression function it is seen that this rule is asymptotically optimal

well posedness and ill posedness of a multidimensional chemotaxis system in the critical besov spaces abstract we study the cauchy problem for a multidimensional chemotaxis system in critical besov spaces b p 1 d p 2 r d b p 1 d p 1 r d d for 1 p 2 d we prove locally well posedness for large initial data and globally well posedness for small initial data of this system and more importantly we show the ill posedness in the sense that a norm inflation phenomenon occurs for p 2 d more precisely we construct a specific initial data which can be arbitrarily small in the besov spaces meanwhile the corresponding solution u can be arbitrarily large after an arbitrarily short time

lagrange structure and dynamics for solutions to the spherically symmetric compressible navier stokes equations the compressible navier stokes system cns with density dependent viscosity coefficients is considered in multi dimension the prototype of the system is the viscous saint venat model for the motion of shallow water a spherically symmetric weak solution to the free boundary value problem for cns with stress free boundary condition and arbitrarily large data is shown to exist globally in time with the free boundary separating fluids and vacuum and propagating at finite speed as particle path which is continuous away from the symmetry center detailed regularity and lagrangian structure of this solution have been obtained in particular it is shown that the particle path is uniquely defined starting from any non vacuum region away from the symmetry center along which vacuum states shall not form in any finite time and the initial regularities of the solution is preserved starting from any non vacuum point at a later on time a particle path is also uniquely defined backward in time which either reaches at some initial non vacuum point or stops at a small middle time and connects continuously with vacuum in addition the free boundary is shown to expand outward at an algebraic rate in time and the fluid density decays and tends to zero almost everywhere away from the symmetry center as the time grows up this finally leads to the formation of vacuum state almost everywhere as the time goes to infinity

global solutions of the navier stokes equations for multidimensional compressible flow with discontinuous initial data abstract we prove the global existence of weak solutions of the navier stokes equations for compressible isothermal flow in two and three space dimensions when the initial density is close to a constant in l 2 and l and the initial velocity is small in l 2 and bounded in l 2 n in two dimensions the l 2 norms must be weighted slightly a great deal of qualitative information about the solution is obtained for example we show that the velocity and vorticity are relatively smooth in positive time as is the effective viscous flux f which is the divergence of the velocity minus a certain multiple of the pressure we find that f plays a crucial role in the entire analysis particularly in closing the required energy estimates understanding rates of regularization near the initial layer and most important obtaining time independent pointwise bounds for the density

mean field theory for car accidents we study analytically the occurrence of car accidents in the nagel schreckenberg traffic model we obtain exact results for the occurrence of car accidents p ac as a function of the car density rho and the degree of stochastic braking p 1 in the case of speed limit v max 1 various quantities are calculated analytically the nontrivial limit p 1 0 is discussed

statistical mechanical approach to fukui ishibashi traffic flow models we consider cellular automaton models for one dimensional traffic flow problems starting with a microscopic relation for the updating rule describing the occupancy on each site of the road a macroscopic evolution relation for the average speed of cars can be obtained by carrying out statistical averages mean field equations are obtained by considering the asymptotic form of the evolution relation this gives the average car speed in the long time limit as a function of the car density the evolution relation is a nonlinear mapping between the average speeds at two consecutive time steps the mean field results can be obtained by studying the attractors of the mapping the approach is applied to study the model recently proposed by fukui and ishibashi our calculations show that for models in which the maximum speed of each car is m a decoupling scheme retaining correlations up to m 1 sites can be applied to the calculation of spatial correlations involving more than m 1 sites exact results are obtained using our approach for models without random delay for models with random delay results are in good agreement with simulation results

global small solutions to an mhd type system the three dimensional case in this paper we consider the global well posedness of a three dimensional incompressible mhd type system with smooth initial data that is close to some nontrivial steady state it is a coupled system between the navier stokes equations and a free transport equation with a universal nonlinear coupling structure the main difficulty of the proof lies in exploring the dissipative mechanism of the system due to the fact that there is a free transport equation of in the coupled equations and only the horizontal derivatives of is dissipative with respect to time to achieve this we first employ anisotropic littlewood paley analysis to establish the key l1 lip 3 estimate to the third component of the velocity field then we prove the global well posedness to this system by the energy method which depends crucially on the divergence free condition of the velocity field 2014 wiley periodicals inc

effects of a type of quenched randomness on car accidents in a cellular automaton model this article reports on a numerical study of the probability pac of the occurrence of car accidents in the nagel schreckenberg ns model with a defect a bottleneck situation bottlenecks results in a distinct variety of traffic flow including saturated flow vehicle queuing changes of traffic flow and variation in the number of stopped cars the authors describe the model used and the conditions for the occurrence of accidents review the numerical studies of the car accidents and consider the effects of the stochastic braking and speed limiting on the probability of car accidents in the deterministic ns model numerical results show that there exists a critical value of car density below which no car accident happens the critical density is not related only to the maximum speed of cars but also to the braking probability at the defect the braking probability at a defect can enhance not suppress the occurrence of car accidents when its value is small only the braking probability at the defect is very large car accidents can be reduced by the bottleneck in the nondeterministic ns model the probability pac exhibits the same behaviors with that in the deterministic model except the case of vmax 1 under which the probability pac is only reduced by the defect the defect also induces the inhomogeneous distribution of car accidents over the whole road car accidents happen only in the high density region

on the influence of gravity on density dependent incompressible periodic fluids abstract the present work is devoted to the analysis of density dependent incompressible fluids in a 3d torus when the froude number e goes to zero we consider the very general case where the initial data do not have a zero horizontal average where we only have smoothing effect on the velocity but not on the density and where we can have resonant phenomena on the domain we explicitly determine the limit system when e 0 and prove its global wellposedness finally we prove that for large initial data the density dependent incompressible fluid system is globally wellposed provided that e is small enough

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

stochastic boundary conditions in the deterministic nagel schreckenberg traffic model we consider open systems where cars move according to the deterministic nagel schreckenberg rules k nagel and m schreckenberg j phys i 2 2221 1992 and with maximum velocity v max 1 which is an extension of the asymmetric exclusion process asep it turns out that the behavior of the system is dominated by two features a the competition between the left and the right boundary b the development of so called buffers due to the hindrance that an injected car feels from the front car at the beginning of the system as a consequence there is a first order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers and the phase diagram essentially differs from that for v max 1 asep

on the role of the besov spaces for the solutions of the generalized burgers equation in homogeneous sobolev spaces abstract the generalized burgers equation tu xxu xuk 1 0 with initial data u0 in homogeneous sobolev spaces are investigated the starting point of this work is the construction of solutions in l 0 b 1 k for small size initial data in b 1 k if in addition the initial data belongs to l p s then the obtained solution is actually in l 0 l p s

zero mach number limit for compressible flows with periodic boundary conditions we address the question of convergence to the incompressible navier stokes equations for slightly compressible viscous flows with ill prepared initial data and periodic boundary conditions the case of the whole space has been studied in an earlier paper by the author the functional setting is very close to the one used by h fujita and t kato for incompressible flows for arbitrarily large initial data we show that the compressible flow with small mach number exists as long as the incompressible one does in particular it exists globally if the corresponding incompressible solution exists for all time we further state a convergence result for the slightly compressible solution filtered by the group of acoustics introduction an engineer would hardly make a distinction between incom pressible flows and slightly compressible flows indeed incompressible navier stokes equations are usually regarded as an appropriate model for describing water in the present paper we study whether such an approximation is relevant from a mathematical viewpoint in the case of periodic boundary conditions the case of the whole space has been treated in 8 after some convenient rescaling see for instance the appendix of 16 or the introduction of 21 the equations for a slightly compressible fluid read

an improved kernel regression method based on taylor expansion many regression functions obtained by nonparametric regression method often appear inconsonance between smoothness and fitness this phenomenon is extremely outstanding near the vertex regions how to improve the fitness and smoothness simultaneously becomes an important problem in the nonparametric regression field in this paper an improved kernel regression is proposed by introducing second derivative estimation into kernel regression function based on taylor expansion theorem experimental results on regression problems show that this new method is feasible and enables us to get regression function that is both smooth and well fitting the application of the method to grey image enhancement indicates that this approach is fruitful to the enhancement of weak information in the images

local in time results for local and non local capillary navier stokes systems with large data abstract in this article we study three capillary compressible models the classical local navier stokes korteweg system and two non local models for large initial data bounded away from zero and with a reference pressure state which is not necessarily stable p can be non positive we prove that these systems have a unique local in time solution and we study the convergence rate of the solutions of the non local models towards the local korteweg model the results are given for constant viscous coefficients and we explain how to extend them for density dependant coefficients

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

relaxation times in the asep model using a dmrg method we compute the largest relaxation times for the totally asymmetric exclusion process tasep with open boundary conditions with a dmrg method this allows us to reach much larger system sizes than in previous numerical studies we are then able to show that the phenomenological theory of the domain wall indeed predicts correctly the largest relaxation time for large systems besides we can obtain results even when the domain wall approach breaks down and show that the kpz dynamical exponent z 3 2 is recovered in the whole maximal current phase

global low energy weak solutions of the equations of three dimensional compressible magnetohydrodynamics we prove the global in time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in l2 and initial density positive and essentially bounded a great deal of information concerning partial regularity is obtained velocity vorticity and magnetic field become relatively smooth in positive time h1 but not h2 and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity thus giving concrete expression to conclusions obtained formally from the rankine hugoniot conditions

exact results for car accidents in a traffic model within the framework of a recent model for car accidents on single lane highway traffic we study analytically the probability of the occurrence of car accidents exact results are obtained various scaling behaviours are observed the linear dependence of the occurrence of car accidents on density is understood as the dominance of a single velocity in the distribution

full velocity difference model for a car following theory in this paper we present a full velocity difference model for a car following theory based on the previous models in the literature to our knowledge the model is an improvement over the previous ones theoretically because it considers more aspects in car following process than others this point is verified by numerical simulation then we investigate the property of the model using both analytic and numerical methods and find that the model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

well posedness of a 3d parabolic hyperbolic keller segel system in the sobolev space framework abstract we investigate global strong solution to a 3 dimensional parabolic hyperbolic system arising from the keller segel model we establish the global well posedness and asymptotic behavior in the energy functional setting precisely speaking if the initial difference between cell density and its mean is small in l 2 and the ratio of the initial gradient of the chemical concentration and the initial chemical concentration is also small in h 1 then they remain to be small in l 2 h 1 for all time moreover if the mean value of the initial cell density is smaller than some constant then the cell density approaches its initial mean and the chemical concentration decays exponentially to zero as t goes to infinity the proof relies on an application of fourier analysis to a linearized parabolic hyperbolic system and the smoothing effect of the cell density and the damping effect of the chemical concentration

scaling of pedestrian channel flow with a bottleneck abstract pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice gas model of biased random walkers it is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density pc with increasing density the flow rate saturates at higher density than the critical density in the choking flow region a scaling behavior is found as follows the saturated flow rate js scales as js d0 93 0 02 and the critical density pc scales as pc d w 1 16 0 02 where d is the width of the bottleneck and w is the width of channel the plot of the rescaled flow rate against the rescaled density collapses onto a single curve

the cauchy problem for the pressureless euler isentropic navier stokes equations we present a new hydrodynamic model consisting of the pressureless euler equations and the isentropic compressible navier stokes equations where the coupling of two systems is through the drag force this coupled system can be derived in the hydrodynamic limit from the particle fluid equations that are frequently used to study the medical sprays aerosols and sedimentation problems for the proposed system we first construct the local in time classical solutions in an appropriate l2l2 sobolev space we also establish the a priori large time behavior estimate by constructing a lyapunov functional measuring the fluctuation of momentum and mass from the averaged quantities and using this together with the bootstrapping argument we obtain the global classical solution the large time behavior estimate asserts that the velocity functions of the pressureless euler and the compressible navier stokes equations are aligned exponentially fast as time tends to infinity

global well posedness for compressible viscoelastic fluids near equilibrium in this paper we prove local well posedness for compressible viscoelastic fluids of the oldroyd model under the assumption that the initial density is bounded away from zero and global well posedness near equilibrium the proof of global well posedness relies on some intrinsic properties of viscoelastic fluids and on a uniform estimate for a linearized hyperbolic parabolic system with convection terms

global existence of strong solution for viscous shallow water system with large initial data on the irrotational part abstract we are interested in studying the cauchy problem for the viscous shallow water system in dimension n 2 we show the existence of global strong solutions with large initial data on the irrotational part of the velocity for the scaling of the equations more precisely our smallness assumption on the initial data is supercritical for the scaling of the equations it allows us to give a first kind of answer to the problem of the existence of global strong solution with large initial energy data in dimension n 2 to do this we introduce the notion of quasi solutions which consists in solving the pressureless viscous shallow water system we can obtain such solutions at least for irrotational data which are subject to regularizing effects both on the velocity and on the density this smoothing effect is purely nonlinear and is crucial in order to build solution of the viscous shallow water system as perturbations of the quasi solutions indeed the pressure term can be considered as a remainder term which becomes small in high frequencies for the scaling of the equations to finish we prove the existence of global strong solution with large initial data when n 2 provided that the mach number is sufficiently large

non existence of classical solutions with finite energy to the cauchy problem of the compressible navier stokes equations the well posedness of classical solutions with finite energy to the compressible navier stokes equations cns subject to arbitrarily large and smooth initial data is a challenging problem in the case when the fluid density is away from vacuum strictly positive this problem was first solved for the cns in either one dimension for general smooth initial data or multi dimension for smooth initial data near some equilibrium state that is small perturbation antontsev et al in boundary value problems in mechanics of nonhomogeneous fluids north holland publishing co amsterdam 1990 kazhikhov in sibirsk mat zh 23 60 64 1982 kazhikhov et al in prikl mat meh 41 282 291 1977 matsumura and nishida in proc jpn acad ser a math sci 55 337 342 1979 j math kyoto univ 20 67 104 1980 commun math phys 89 445 464 1983 in the case that the flow density may contain a vacuum the density can be zero at some space time point it seems to be a rather subtle problem to deal with the well posedness problem for cns the local well posedness of classical solutions containing a vacuum was shown in homogeneous sobolev space without the information of velocity in l2 norm for general regular initial data with some compatibility conditions being satisfied initially cho et al in j math pures appl 9 83 243 275 2004 cho and kim in j differ equ 228 377 411 2006 manuscr math 120 91 129 2006 choe and kim in j differ equ 190 504 523 2003 and the global existence of a classical solution in the same space is established under the additional assumption of small total initial energy but possible large oscillations huang et al in commun pure appl math 65 549 585 2012 however it was shown that any classical solutions to the compressible navier stokes equations in finite energy inhomogeneous sobolev space cannot exist globally in time since it may blow up in finite time provided that the density is compactly supported xin in commun pure appl math 51 229 240 1998 in this paper we investigate the well posedess of classical solutions to the cauchy problem of navier stokes equations and prove that the classical solution with finite energy does not exist in the inhomogeneous sobolev space for any short time under some natural assumptions on initial data near the vacuum this implies in particular that the homogeneous sobolev space is as crucial as studying the well posedness for the cauchy problem of compressible navier stokes equations in the presence of a vacuum at far fields even locally in time

global existence and minimal decay regularity for the timoshenko system the case of non equal wave speeds abstract as a continued work of 18 we are concerned with the timoshenko system in the case of non equal wave speeds which admits the dissipative structure of regularity loss firstly with the modification of a priori estimates in 18 we construct global solutions to the timoshenko system pertaining to data in the besov space with the regularity s 3 2 owing to the weaker dissipative mechanism extra higher regularity than that for the global in time existence is usually imposed to obtain the optimal decay rates of classical solutions so it is almost impossible to obtain the optimal decay rates in the critical space to overcome the outstanding difficulty we develop a new frequency localization time decay inequality which captures the information related to the integrability at the high frequency part furthermore by the energy approach in terms of high frequency and low frequency decomposition we show the optimal decay rate for timoshenko system in critical besov spaces which improves previous works greatly

global existence for the multi dimensional compressible viscoelastic flows abstract the global solutions in critical spaces to the multi dimensional compressible viscoelastic flows are considered the global existence of the cauchy problem with initial data close to an equilibrium state is established in besov spaces using uniform estimates for a hyperbolic parabolic linear system with convection terms we prove the global existence in the besov space which is invariant with respect to the scaling of the associated equations several important estimates are achieved including a smoothing effect on the velocity and the l 1 decay of the density and deformation gradient

traffic accidents in a cellular automaton model with a speed limit zone in this paper we numerically study the probability pac of the occurrence of car accidents in the nagel schreckenberg ns model with a speed limit zone numerical results show that the probability for car accidents to occur pac is determined by the maximum speed v max of the speed limit zone but is independent of the length lv of the speed limit zone in the deterministic ns model however in the nondeterministic ns model the probability of the occurrence of car accidents pac is determined not only by the maximum speed v max but also the length lv the probability pac increases accordingly with the increase of the maximum speed of the speed limit zone but decreases with the increase of the length of the speed limit zone in the low density region however in the case of v max 1 the probability pac increases with the increase of the length in the low density region but decreases in the interval between the low density and high density regions the speed limit zone also causes an inhomogeneous distribution of car accidents over the whole road theoretical analyses give an agreement with numerical results in the nondeterministic ns model with v max 1 and vmax 5

nondeterministic nagel schreckenberg traffic model with open boundary conditions we study the phases of the nagel schreckenberg traffic model with open boundary conditions as a function of the randomization probabilities pg0 and the maximum velocity v mathrm max g1 due to the existence of buffer sites which enhance the free flow region the behavior is much richer than that of the related parallel updated asymmetric exclusion process asep v mathrm max 1 such sites exist for v mathrm max g 3 and pl p c where the phase diagram is qualitatively similar to the p 0 case there is a free flow and a jamming phase separated by a line of first order transitions for pg p c an additional maximum current phase separated by second order transitions occurs like for the asep the density profile decays in the maximum current phase algebraically with an exponent ensuremath gamma ensuremath approx frac 2 3 for all v mathrm max g 2 indicating that these models belong to another universality class than the asep where ensuremath gamma frac 1 2

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

some uniform estimates and blowup behavior of global strong solutions to the stokes approximation equations for two dimensional compressible flows abstract this paper concerns the global existence and the large time behavior of strong and classical solutions to the two dimensional 2d stokes approximation equations for the compressible flows we consider the unique global strong solution or classical solution to the 2d stokes approximation equations for the compressible flows together with the space periodicity boundary condition or the no stick boundary condition or cauchy problem for arbitrarily large initial data first we prove that the density is bounded from above independent of time in all these cases secondly we show that for the space periodicity boundary condition or the no stick boundary condition if the initial density contains vacuum at least at one point then the global strong or classical solution must blow up as time goes to infinity

optimal decay rate for strong solutions in critical spaces to the compressible navier stokes equations abstract in this paper we are concerned with the convergence rates of the global strong solution to motionless state with constant density for the compressible navier stokes equations in the whole space r n for n 3 it is proved that the perturbations decay in critical spaces if the initial perturbations of density and velocity are small in b 2 1 n 2 r n b 1 0 r n and b 2 1 n 2 1 r n b 1 0 r n respectively

restoration of images corrupted by gaussian and uniform impulsive noise many approaches to image restoration are aimed at removing either gaussian or uniform impulsive noise this is because both types of degradation processes are distinct in nature and hence they are easier to manage when considered separately nevertheless it is possible to find them operating on the same image which produces a hard damage this happens when an image already contaminated by gaussian noise in the image acquisition procedure undergoes impulsive corruption during its digital transmission here we propose a principled method to remove both types of noise it is based on a bayesian classification of the input pixels which is combined with the kernel regression framework

global well posedness for compressible navier stokes equations with highly oscillating initial velocity in this paper we prove global well posedness for compressible navier stokes equations in the critical functional framework with the initial data close to a stable equilibrium this result allows us to construct global solutions for the highly oscillating initial velocity the proof relies on a new estimate for the hyperbolic parabolic system with convection terms 2010 wiley periodicals inc

analyticity of solutions to the barotropic compressible navier stokes equations abstract in this paper we establish analyticity of solutions to the barotropic compressible navier stokes equations describing the motion of the density and the velocity field u in r 3 we assume that 0 is a small perturbation of 1 and 1 1 0 u 0 are analytic in besov spaces with analyticity radius 0 we show that the corresponding solutions are analytic globally in time when 1 1 0 u 0 are sufficiently small to do this we introduce the exponential operator e t d acting on 1 1 u where d is the differential operator whose fourier symbol is given by 1 1 2 3 and t is chosen to satisfy t globally in time

the incompressible limit in l p type critical spaces this paper aims at justifying the low mach number convergence to the incompressible navier stokes equations for viscous compressible flows in the ill prepared data case the fluid domain is either the whole space or the torus a number of works have been dedicated to this classical issue all of them being to our knowledge related to l 2 spaces and to energy type arguments in the present paper we investigate the low mach number convergence in the l p type critical regularity framework more precisely in the barotropic case the divergence free part of the initial velocity field just has to be bounded in the critical besov space dot b d p 1 p r cap dot b 1 infty 1 for some suitable p r in 2 4 times 1 infty we still require l 2 type bounds on the low frequencies of the potential part of the velocity and on the density though an assumption which seems to be unavoidable in the ill prepared data framework because of acoustic waves in the last part of the paper our results are extended to the full navier stokes system for heat conducting fluids

the influence of tollbooths on highway traffic we study the effects of tollbooths on the traffic flow various types of toll collection are examined which can be characterized either by a waiting time or a reduced speed the phase separation results in a saturated flow which is observed as a plateau region in the fundamental diagram the effects of lane expansion near the tollbooth are examined the full capacity of a highway can be restored besides the numerical results we also obtain analytical expressions for various quantities