on the structural stability of the euler voigt and navier stokes voigt models abstract we consider the euler voigt equations and the navier stokes voigt equations which are obtained by an inviscid regularization from the corresponding equations the main result we show is the structural stability of the system in terms of the variations of both viscosity and regularization parameters

local well posedness of the incompressible euler equations in b 11 and the inviscid limit of the navier stokes equations abstract we prove the inviscid limit of the incompressible navier stokes equations in the same topology of besov spaces as the initial data the proof is based on proving the continuous dependence of the navier stokes equations uniformly with respect to the viscosity to show the latter we rely on some bona smith type argument in the l p setting our obtained result implies a new result that the cauchy problem of the euler equations is locally well posed in the borderline besov space b 1 1 r d d 2 in the sense of hadmard which is an open problem left in recent works by bourgain and li in 3 4 and by misiolek and yoneda in 12 13 14

convergence analysis for operator splitting methods applied to conservation laws with stiff source terms we analyze the order of convergence for operator splitting methods applied to conservation laws with stiff source terms we suppose that the source term q u is dissipative it is proved that the l 1 error introduced by the time splitting can be bounded by o d t vert q u 0 vert l 1 which is an improvement of the o q d t upper bound where d t is the splitting time step q is the lipschitz constant of q or q max u vert q u vert in case q is smooth a generic model with a special form of stiff source is also investigated we propose a nonuniform temporal mesh to eliminate the effect of the initial layer introduced by the stiff source term our results are derived by using parabolic regularizations rather than using kuznetsov s approximation theory which has been employed as a standard approach for error analysis to the dimensional or time splitting methods numerical examples are presented to illustrate the theoretical results

on the stationary solutions and inviscid limit for the generalized proudman johnson equation with o 1 forcing abstract we consider the stationary problem for the generalized proudman johnson equation x x x a x x x x x x x f where a r and 0 are parameters and and f satisfy the periodic boundary conditions on we establish the existence of a time dependent solution and the uniqueness of the stationary solution for some large then we investigate the behavior of solution sequences in the limit 0 fixing a and f where bifurcations appear and new solutions emerge in particular we analyze if there is convergence towards stationary solutions for the corresponding inviscid equation

on the evolution of nearly circular vortex patches recently the classical problem of the evolution of patches of constant vorticity was reformulated as an evolution equation for the boundary of the patch we study this equation in the neighborhood of the circular vortex patch and introduce a hierarchy of area preserving nonlinear approximate equations the first of these equations is shown to have a rich rigid structure it possesses an exhaustive increasing sequence of linear invariant manifolds of arbitrarily large finite dimensions on each of these manifolds the equation can be written as an explicit finite system of ordinary differential equations solutions of these odes starting from arbitrarily small neighborhoods of the circular vortex patch are shown to blow up

hidden markov models and disease mapping we present new methodology to extend hidden markov models to the spatial domain and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon this situation occurs commonly in many domains of application particularly in disease mapping we assume that the counts follow a poisson model at the lowest level of the hierarchy and introduce a finite mixture model for the poisson rates at the next level the novelty lies in the model for allocation to the mixture components which follows a spatially correlated process the potts model and in treating the number of components of the spatial mixture as unknown inference is performed in a bayesian framework using reversible jump markov chain monte carlo the model introduced can be viewed as a bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models performance of the model and comparison with an alternative well known markov random field specification for the poisson rates are de

on the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half plane we consider the navier stokes equations for viscous incompressible flows in the half plane under the no slip boundary condition by using the vorticity formulation we prove the local in time convergence of the navier stokes flows to the euler flows outside a boundary layer and to the prandtl flows in the boundary layer in the inviscid limit when the initial vorticity is located away from the boundary 2014 wiley periodicals inc

contour dynamics of incompressible 3 d fluids in a porous medium with different densities we consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium which is known as the muskat problem and in two dimensions it is mathematically analogous to the two phase hele shaw cell we focus on a fluid interface given by a jump of densities being the equation of the evolution obtained using darcy s law we prove local well posedness when the smaller density is above stable case and in the unstable case we show ill posedness

numerical methods for hyperbolic conservation laws with stiff relaxation ii higher order godunov methods a higher order godunov method is presented for hyperbolic systems of conservation laws with stiff relaxing source terms the goal is to develop a godunov method that produces higher order accurate

numerical approximation of entropy solutions for hyperbolic integro differential equations scalar hyperbolic integro differential equations arise as models for e g radiating or self gravitating fluid flow we present finite volume schemes on unstructured grids applied to the cauchy problem for such equations for a rather general class of integral operators we show convergence of the approximate solutions to a possibly discontinuous entropy solution of the problem for a specific model problem in radiative hydrodynamics we introduce a convergent fully discrete finite volume scheme under the assumption of sufficiently fast spatial decay of the entropy solution we can even establish the convergence rate h1 4 ln h where h denotes the grid parameter the convergence proofs rely on appropriate variants of the classical kruzhkov method for local balance laws together with a truncation technique to cope with the nonlocal character of the integral operator

reducing slip boundary value problems from the half to the whole space applications to inviscid limits and to non newtonian fluids abstract the study of a very large class of linear and non linear stationary and evolutive partial differential problems in the half space or similar under the slip boundary condition is reduced here to the much simpler study of the corresponding results for the same problem in the whole space the approach is particularly suitable for proving new results in strong norms to determine whether this extension is available turns out to be a simple exercise the verification depends on a few general features of the functional space x related to the space variables hence we present an approach as much as possible independent of the particular space x we appeal to a reflection technique hence a crucial assumption is to be in the presence of flat boundaries see below instead of stating general theorems we rather prefer to illustrate how to apply our results by considering a couple of interesting problems as a main example we show that sharp vanishing viscosity limit results that hold for the evolution navier stokes equations in the whole space can be extended to the slip boundary value problem in the half space we also show some applications to non newtonian fluid problems

local regularity for the modified sqg patch equation we study the patch dynamics on the whole plane and on the half plane for a family of active scalars called modified surface quasi geostrophic sqg equations these involve a parameter that appears in the power of the kernel in their biot savart laws and describes the degree of regularity of the equation the values 0 and correspond to the two dimensional euler and sqg equations respectively we establish here local in time regularity for these models for all 0 on the whole plane and for all small 0 on the half plane we use the latter result in 16 where we show existence of regular initial data on the half plane that lead to a finite time singularity 2016 wiley periodicals inc

the limit of vanishing viscosity for the incompressible 3d navier stokes equations with helical symmetry abstract in this paper we are concerned with the vanishing viscosity problem for the three dimensional navier stokes equations with helical symmetry in the whole space we choose viscosity dependent initial u 0 with helical swirl an analogue of the swirl component of axisymmetric flow of magnitude o in the l 2 norm we assume u 0 u 0 in h 1 the new ingredient in our analysis is a decomposition of helical vector fields through which we obtain the required estimates

local in time existence and uniqueness of solutions to the prandtl equations by energy methods we prove local existence and uniqueness for the two dimensional prandtl system in weighted sobolev spaces under oleinik s monotonicity assumption in particular we do not use the crocco transform or any change of variables our proof is based on a new nonlinear energy estimate for the prandtl system this new energy estimate is based on a cancellation property that is valid under the monotonicity assumption to construct the solution we use a regularization of the system that preserves this nonlinear structure this new nonlinear structure may give some insight into the convergence properties from the navier stokes system to the euler system when the viscosity goes to 0 2015 wiley periodicals inc

a note on overdispersed exponential families abstract the issue of creating overdispersion in a given one parameter one dimensional exponential family by extending it to a two parameter exponential family with the same support is considered an easily verifiable sufficient condition for this is derived it is shown that a large class of families satisfy this condition and that this class includes efron s 1986 and lindsay s 1986 family as special cases this class is also closely related to jorgensen s 1988 exponential dispersion models ump unbiased tests for testing overdispersion are exhibited and it is shown that in this context cox s overdispersion test is a special case a graphical display is developed to select a family of the general class which should be used with a given set of data to overdisperse a given target one parameter family two real data illustrations are given kr

inviscid limit for damped and driven incompressible navier stokes equations in mathbb r 2 we consider the zero viscosity limit of long time averages of solutions of damped and driven navier stokes equations in mathbb r 2 we prove that the rate of dissipation of enstrophy vanishes stationary statistical solutions of the damped and driven navier stokes equations converge to renormalized stationary statistical solutions of the damped and driven euler equations these solutions obey the enstrophy balance

initial boundary layer associated with the nonlinear darcy brinkman oberbeck boussinesq system abstract in this paper we study the vanishing darcy number limit of the nonlinear darcy brinkman oberbeck boussinesq system dbob this singular perturbation problem involves singular structures both in time and in space giving rise to initial layers boundary layers and initial boundary layers we construct an approximate solution to the dbob system by the method of multiple scale expansions the convergence with optimal convergence rates in certain sobolev norms is established rigorously via the energy method

numerical study of a flow of regular planar curves that develop singularities at finite time in this paper we will study the following geometric flow obtained by goldstein and petrich while considering the evolution of a vortex patch in the plane under euler s equations mathbf x t k s mathbf n frac 1 2 k 2 mathbf t with s being the arc length parameter and k the curvature perelman and vega proved in j differential equations 235 2007 pp 56 73 that this flow has a one parameter family of regular solutions that develop a corner shaped singularity at finite time we will give a method for reproducing numerically the evolution of those solutions as well as the formation of the corner showing several properties associated to them

interaction of vortices in weakly viscous planar flows we consider the inviscid limit for the two dimensional incompressible navier stokes equation in the particular case where the initial flow is a finite collection of point vortices we suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter and we choose a time t 0 such that the helmholtz kirchhoff point vortex system is well posed on the interval 0 t under these assumptions we prove that the solution of the navier stokes equation converges as 0 to a superposition of lamb oseen vortices whose centers evolve according to a viscous regularization of the point vortex system convergence holds uniformly in time in a strong topology which allows us to give an accurate description of the asymptotic profile of each individual vortex in particular we compute to leading order the deformations of the vortices due to mutual interactions this makes it possible to estimate the self interactions which play an important role in the convergence proof

initial boundary layer associated with the nonlinear darcy brinkman system abstract we study the interaction of initial layer and boundary layer in the nonlinear darcy brinkman system in the vanishing darcy number limit in particular we show the existence of a function of corner layer type so called initial boundary layer in the solution of the nonlinear darcy brinkman system an approximate solution is constructed by the method of multiple scale expansion in space and in time we establish the optimal convergence rates in various sobolev norms via energy method

an error estimate for finite volume methods for multidimensional conservation laws in this paper an l ll error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained these methods can be formally high order accurate and are defined on general triangulations the error is proven to be of order ft 4 where h represents the size of the mesh via an extension of kuznetsov approximation theory for which no estimate of the total variation and of the modulus of con tinuity in time are needed the result is new even for the finite volume method constructed from monotone numerical flux functions

convergence of the finite volume method for multidimensional conservation laws we establish the convergence of the finite volume method applied to multidimensional hyperbolic conservation laws and based on monotone numerical flux functions our technique applies with a fairly unrestrictive assumption on the triangulations flat elements are allowed and to lipschitz continuous flux functions we treat the initial and boundary value problem and obtain the strong convergence of the scheme to the unique entropy discontinuous solution in the sense of kruzkov the proof of convergence is based on a convergence framework coquel and lefloch math comp 57 1991 pp 169 210 and j numer anal 30 1993 pp 675 700 from a convex decomposition of the scheme we derive a new estimate for the rate of entropy dissipation and a new formulation of the discrete entropy inequalities these estimates are shown to be sufficient for the passage to the limit in the discrete equation convergence follows from diperna s uniqueness result in the class of entropy measure valued solutions

the inviscid limit in the cauchy problem of the inhomogeneous incompressible navier stokes equations abstract applying similar arguments as introduced in bona smith 4 we mainly study the inviscid limit of the inhomogeneous incompressible navier stokes equations in r d some results of local uniform estimates on solutions of the navier stokes equations independent of the viscosity are also obtained

first and second order error estimates for the upwind source at interface method the upwind source at interface method for hyperbolic conservation laws with source term introduced in b perthame c simeoni convergence of the upwind interface source method for hyperbolic conservation laws hyperbolic problems theory numerics applications t hou and e tadmor eds springer 2003 is essentially first order accurate under appropriate hypotheses of consistency on the finite volume discretization of the source term we prove l p error estimates 1 le p infty in the case of a uniform spatial mesh for which an optimal result can be obtained we thus conclude that the same convergence rates hold as for the corresponding homogeneous problem to improve the numerical accuracy we develop two different approaches of dealing with the source term and we discuss the question of deriving second order error estimates numerical evidence shows that those techniques produce high resolution schemes compatible with the upwind source at interface method

self similar 2d euler solutions with mixed sign vorticity we construct a class of self similar 2d incompressible euler solutions that have initial vorticity of mixed sign the boundaries between regions of positive and negative vorticity form algebraic spirals similar to the kaden spiral and as opposed to prandtl s logarithmic vortex spirals also unlike the prandtl case spirals are not initially present

remarques sur l instabilite du probleme des poches de tourbillon resume nous etudions le probleme des poches de tourbillon pour des contours initiaux poches du cercle unite une approximation quadratique de l equation d evolution se revele instable en temps fini la norme lipschitz du contour devenant arbitrairement grande

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

global regularity of 2d density patches for inhomogeneous navier stokes this paper is about lions open problem on density patches lions in mathematical topics in fluid mechanics vol 1 volume 3 of oxford lecture series in mathematics and its applications clarendon press oxford university press new york 1996 whether or not inhomogeneous incompressible navier stokes equations preserve the initial regularity of the free boundary given by density patches using classical sobolev spaces for the velocity we first establish the propagation of c 1 gamma regularity with 0 gamma 1 in the case of positive density furthermore we go beyond this to show the persistence of a geometrical quantity such as the curvature in addition we obtain a proof for c 2 gamma regularity

a generalized linear models approach to spatial scan statistics for covariate adjustment the spatial scan statistic proposed by kulldorff commun statist theory methods 1997 26 1481 1496 is one of the most widely used methods for detecting spatial clusters and evaluating their statistical significance however it is not fully capable of adjusting for all types of confounding covariates in this article a generalized linear models glm approach to construct spatial scan statistics which is readily in a form for covariate adjustment is proposed using glm spatial scan statistics for different probability models can be formulated in a single framework the test statistic is based on the log likelihood ratio test statistic and evaluated using monte carlo hypothesis testing the proposed method is illustrated using texas female breast cancer data concerning late versus early stage cancer cases with covariates of race ethnicity and age group

contour dynamics for the euler equations in two dimensions we present a contour dynamics algorithm for the euler equations of fluid dynamics in two dimensions this is applied to regions of piecewise constant vorticity withinfinite area vortexregions favrs essentially this reduces the dimensionality by one and we are treating the interaction of closed polygonal contours whose nodes are advected by the total fluid motion computed self consistently a leapfrog centered scheme is used for temporal advancement computer simulation results are given for two and four like signed interacting favrs in all cases wavelike surface deformations are observed if the distance between favrs is comparable to their extent diameter these surface deformations are large they play an essential role in the observed coalescence of favrs

existence and uniqueness of two dimensional euler poisson system and wkb approximation to the nonlinear schrodinger poisson system in this paper we study a dispersive euler poisson system in two dimensional euclidean space our aim is to show unique existence and the zero dispersion limit of the time local weak solution since one may not use dispersive structure in the zero dispersion limit when reducing the regularity lack of critical embedding h1 l becomes a bottleneck we hence employ an estimate on the best constant of the gagliardo nirenberg inequality by this argument a reasonable convergence rate for the zero dispersion limit is deduced with a slight loss we also consider the semiclassical limit problem of the schrodinger poisson system in two dimensions

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

note on loss of regularity for solutions of the 3 d incompressible euler and related equations one of the central problems in the mathematical theory of turbulence is that of breakdown of smooth indefinitely differentiable solutions to the equations of motion in 1934 j leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3 d incompressible navier stokes equations the problem is still open we show in this report that breakdown of smooth solutions to the 3 d incompressible slightly viscous i e corresponding to high reynolds numbers or highly turbulent navier stokes equations cannot occur without breakdown in the corresponding solution of the incompressible euler ideal fluid equation we prove then that solutions of distorted euler equations which are equations closely related to the euler equations for short term intervals do breakdown

error bounds for fractional step methods for conservation laws with source terms fractional step methods have been used to approximate solutions of scalar conservation laws with source terms in this paper the stability and accuracy of the basic fractional step algorithms are analyzed when these algorithms are used to compute discontinuous solutions of nonhomogeneous scalar conservation laws the authors show that time splitting methods for conservation laws with source terms always converge to the unique weak solution satisfying the entropy condition in particular it is proved that the l 1 errors in the splitting methods are bounded by o sqrt delta t where delta t is the splitting time step the l 1 convergence rate of a class of fully discrete splitting methods is also investigated

a new boundary condition for the three dimensional navier stokes equation and the vanishing viscosity limit in this paper we propose a new vorticity boundary condition for the three dimensional incompressible navier stokes equation for a general smooth domain in r3 this boundary condition is motivated by the generalized navier slip boundary condition involving the vorticity it is shown first that such an initial boundary value problem is well posed at least local in time furthermore more importantly we obtain some estimates on rate of convergence in c 0 t h1 and c 0 t h2 of the solutions to the corresponding solutions of the ideal euler equations with the standard slip boundary condition

the euler limit of the navier stokes equations and rotating fluids with boundary in this paper we study the convergence of weak solutions of the navier stokes equations in some particular domains with different horizontal and vertical viscosities when they go to zero with different speeds the difficulty here comes from the dirichlet boundary conditions precisely we show that if the ratio of the vertical viscosity to the horizontal viscosity also goes to zero then the solutions converge to the solution of the euler system we study the same limit for rotating fluids with rossby number also going to zero

inviscid limit for the damped boussinesq equation abstract in this paper we consider the limit behavior of solutions to the cauchy problem for damped boussinesq equation in the regime of small viscosity in r n it is shown that the strong solutions of damped boussinesq equation converge to a strong solution of boussinesq equation in any time interval 0 t the key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped boussinesq equation which is a kind of new view we analyze the dispersion by the techniques of high low frequency decomposition and littlewood paley dyadic decomposition stationary phase estimate and some properties of bessel function

boundary layer associated with the darcy brinkman boussinesq model for convection in porous media abstract we study the asymptotic behavior of the infinite darcy prandtl number darcy brinkman boussinesq system for convection in porous media at a small brinkman darcy number the existence of a boundary layer with thickness proportional to the square root of the brinkman darcy number for the velocity field is established in both the l h 1 norm in 2 and 3 d and the l l norm in 2d this improves in several respects an earlier result of payne and straughan 1998 60 where the vanishing brinkman darcy number limit is studied without resolving the boundary layer

on the vanishing viscosity limit of 3d navier stokes equations under slip boundary conditions in general domains we consider the vanishing viscosity limit for the navier stokes equations with certain slip without friction boundary conditions in a bounded domain with non flat boundary in particular we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary the proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

weak strong uniqueness for measure valued solutions we prove the weak strong uniqueness for measure valued solutions of the incompressible euler equations these were introduced by diperna and majda in their landmark paper commun math phys 108 4 667 689 1987 where in particular global existence to any l2 initial data was proven whether measure valued solutions agree with classical solutions if the latter exist has apparently remained open

zygmund spaces inviscid limit and uniqueness of euler flows the paper improves the classical uniqueness result for the incompressible euler system in the n dimensional case assuming that nabla u e in l 1 0 t it bmo omega only moreover the rate of the convergence for the inviscid limit of solutions to the navier stokes equations is obtained under the same regularity of the limit eulerian flow a key element of the proof is a logarithmic inequality between the hardy and l 1 spaces which is a consequence of the basic properties of the zygmund space l ln l

global regularity for vortex patches we present a proof of chemin s 4 result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth

doubly connected v states for the generalized surface quasi geostrophic equations in this paper we prove the existence of doubly connected v states for the generalized sqg equations with 0 1 they can be described by countable branches bifurcating from the annulus at some explicit eigenvalues related to bessel functions of the first kind contrary to euler equations hmidi et al doubly connected v states for the planar euler equations arxiv 1409 7096 2015 we find v states rotating with positive and negative angular velocities at the end of the paper we discuss some numerical experiments concerning the limiting v states

spatial scan statistics with overdispersion the spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection for more than a decade however overdispersion often presents in real world data causing not only violation of the poisson assumption but also excessive type i errors or false alarms in order to account for overdispersion we extend the poisson based spatial scan test to a quasi poisson based test the simulation shows that the proposed method can substantially reduce type i error probabilities in the presence of overdispersion in a case study of infant mortality in jiangxi china both tests detect a cluster however a secondary cluster is identified by only the poisson based test it is recommended that a cluster detected by the poisson based scan test should be interpreted with caution when it is not confirmed by the quasi poisson based test copyright 2011 john wiley sons ltd

on the blow up criterion of 3d navier stokes equations abstract in this paper we prove some properties of the maximal solution of navier stokes equations if the maximum time t is finite we establish that the growth of u t h s is at least of the order of t t s 3 see eq 1 4 also we give some new blow up results specific properties and standard techniques are used

zero viscosity limit of the incompressible navier stokes equations with sharp vorticity gradient abstract it is well known that the 3d incompressible euler equations admit some local in time solutions for which the vorticity is piecewise smooth and discontinuous across a smooth time dependent hypersurface which evolves with the flow in this paper we prove that such a solution can be obtained as zero viscosity limit of strong solutions to the navier stokes equations whose vorticity has sharp variations near the hypersurface associated with the inviscid limit indeed we exhibit some sequences of exact solutions to the navier stokes equations with vanishing viscosity which are given by multi scale asymptotic expansions involving some characteristic boundary layers given by some linear pdes the convergence and the validity of the expansion are guaranteed on the time interval associated with the solution to the euler equations

vanishing diffusivity limit for the 3d heat conductive boussinesq equations with a slip boundary condition abstract in this paper we consider the 3d heat conductive boussinesq equations with a slip boundary condition for the velocity field and neumann boundary condition for the temperature we prove that there exists an interval of time which is uniform for the heat conductivity coefficient and for which the 3d heat conductive boussinesq equations have a strong solution the solution is uniformly bounded in some spaces with respect to based on these uniform estimates we establish the vanishing diffusivity limit for the boussinesq equations and also obtain the convergence rates for the velocity field and the temperature

numerical methods for hyperbolic conservation laws with stiff relaxation i spurious solutions the author considers the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed uniform spatial grid it is conjectured that certain a priori criteria ensure that the numerical method does not produce spurious solutions as the relaxation time vanishes one criterion is that the limits of vanishing relaxation time and vanishing viscosity commute for the viscous regularization of the hyperbolic system a second criterion is that a certain subcharacteristic condition be satisfied by the hyperbolic system this conjecture is supported with analytical and numerical results for a specific example the solution of generalized riemann problems of a model system of equations with a fractional step scheme in which godunov s method is coupled with the backward euler method similar ideas are applied to the numerical solution of stiff detonation problems

attractors of the velocity vorticity voigt model of the 3d navier stokes equations with damping abstract in this paper we prove the existence of global and exponential attractors of optimal regularity of a regularization for the three dimensional navier stokes equations with damping which is called the three dimensional velocity vorticity voigt vvv system proposed by larios pei and rebholz larios et al 2019 differently there is no voigt term 2 a w t in the second equation of system 1 1 below the proof is based on some energy estimates in sobolev spaces and the semigroup decomposition

local and global existence of smooth solutions for the stochastic euler equations with multiplicative noise we establish the local existence of pathwise solutions for the stochastic euler equations in a three dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise in the two dimensional case we obtain the global existence of these solutions with additive or linear multiplicative noise finally we show that in the three dimensional case the addition of linear multiplicative noise provides a regularizing effect the global existence of solutions occurs with high probability if the initial data is sufficiently small or if the noise coefficient is sufficiently large

uniform regularity and vanishing viscosity limit for the free surface navier stokes equations we study the inviscid limit of the free boundary navier stokes equations we prove the existence of solutions on a uniform time interval by using a suitable functional framework based on sobolev conormal spaces this allows us to use a strong compactness argument to justify the inviscid limit our approach does not rely on the justification of asymptotic expansions in particular we get a new existence result for the euler equations with free surface from the one for navier stokes

remarks about the inviscid limit of the navier stokes system in this paper we prove two results about the inviscid limit of the navier stokes system the first one concerns the convergence in hs of a sequence of solutions to the navier stokes system when the viscosity goes to zero and the initial data is in hs the second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions we present here a simple proof which also works in the 3d case the 3d case is new

uniform regularity and relaxation limit for the outer pressure problem of gas dynamics with several thermal nonequilibrium modes abstract we study in this paper the uniform regularity and relaxation limit for the outer pressure problem of one dimensional gas dynamics with several thermal nonequilibrium modes the uniform regularity is established for the initial data satisfying the compatible conditions on the boundary the relaxation limit to equilibrium flow or frozen flow is also investigated by a compactness argument

on the convergence rate of the euler α an inviscid second grade complex fluid model to the euler equations we study the convergence rate of the solutions of the incompressible euler an inviscid second grade complex fluid equations to the corresponding solutions of the euler equations as the regularization parameter approaches zero first we show the convergence in hs s n 2 1 in the whole space and that the smooth euler solutions exist at least as long as the corresponding solution of the euler equations next we estimate the convergence rate for two dimensional vortex patch with smooth boundaries

vanishing viscosity limit to the planar rarefaction wave for the two dimensional full compressible navier stokes equations abstract the vanishing viscosity limit for the multi dimensional compressible navier stokes equations to the corresponding euler equations is a difficult and challenging problem in the mathematics recently l li d wang and y wang 17 verified that the solutions for the 2d compressible isentropic navier stokes equations converge to the planar rarefaction wave solution for the corresponding 2d euler equations as viscosity vanishes with a convergence rate 1 6 ln in this paper the vanishing viscosity limit of 2d non isentropic compressible navier stokes equations is studied in contrast to the work 17 the convergence rate for the 2d full compressible navier stokes equations is improved to 2 7 ln 2 by choosing a different scaling argument and performing more detailed energy estimates

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

nonlocal systems of conservation laws in several space dimensions we present a lax friedrichs type algorithm to numerically integrate a class of nonlocal and nonlinear systems of conservation laws in several space dimensions the convergence of the approximate solutions is proved also providing the existence of a solution in a slightly more general setting than in other results in the current literature an application to a crowd dynamics model is considered

research and development competition and innovation pseudo maximum likelihood and simulated maximum likelihood methods applied to count data models with heterogeneity abstract this paper focuses on the relationship between the research and development r d expenditures undertaken by firms and the number of patents claimed by them the econometric methods we use incorporate two important features of the data first we introduce a heterogeneity term accounting for the unobservable factors affecting the production of innovations second we allow for a large proportion of the sample not to apply for a patent depending on the specification estimation proceeds by maximum likelihood pseudo maximum likelihood or simulated maximum likelihood methods our main findings are the following i the returns to scale in the innovation technology may be constant on average and ii competitors r d may have a negative impact on own innovation thus revealing a rivalry effect of intellectual property

finite volume schemes for nonhomogeneous scalar conservation laws error estimate in this paper we study finite volume schemes for the nonhomogeneous scalar conservation law u t rm div f x t u q x t u with initial condition u x 0 u0 x the source term may be either stiff or nonstiff in both cases we prove error estimates between the approximate solution given by a finite volume scheme the scheme is totally explicit in the nonstiff case semi implicit in the stiff case and the entropy solution the order of these estimates is h frac 1 4 in space time l 1 norm h denotes the size of the mesh furthermore the error estimate does not depend on the stiffness of the source term in the stiff case

uniform regularity and vanishing dissipation limit for the full compressible navier stokes system in three dimensional bounded domain in the present paper we study the uniform regularity and vanishing dissipation limit for the full compressible navier stokes system whose viscosity and heat conductivity are allowed to vanish at different orders the problem is studied in a three dimensional bounded domain with navier slip type boundary conditions it is shown that there exists a unique strong solution to the full compressible navier stokes system with the boundary conditions in a finite time interval which is independent of the viscosity and heat conductivity the solution is uniformly bounded in w 1 infty and is a conormal sobolev space based on such uniform estimates we prove the convergence of the solutions of the full compressible navier stokes to the corresponding solutions of the full compressible euler system in l infty 0 t l 2 l infty 0 t h 1 and l infty 0 t times omega with a rate of convergence

an elliptic spatial scan statistic the spatial scan statistic is commonly used for geographical disease cluster detection cluster evaluation and disease surveillance the most commonly used shape of the scanning window is circular in this paper we explore an elliptic version of the spatial scan statistic using a scanning window of variable location shape eccentricity angle and size and with and without an eccentricity penalty the method is applied to breast cancer mortality data from northeastern united states and female oral cancer mortality in the united states power comparisons are made with the circular scan statistic

on convergence of numerical schemes for hyperbolic conservation laws with stiff source terms we deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms we suppose that the source term is dissipative but it is not necessarily a lipschitzian function the convergence of the approximate solution towards the entropy solution is established for first and second order accurate muscl and for splitting semi implicit methods

vanishing viscosity limit for homogeneous axisymmetric no swirl solutions of stationary navier stokes equations abstract 1 homogeneous axisymmetric no swirl solutions of three dimensional incompressible stationary navier stokes equations which are smooth on the unit sphere minus the north and south poles have been classified in this paper we study the vanishing viscosity limit of sequences of these solutions as the viscosity tends to zero some sequences of solutions c l o c m converge to solutions of euler equations on the sphere minus the poles while for other sequences of solutions transition layer behaviors occur for every latitude circle there are sequences which c l o c m converge respectively to different solutions of the euler equations on the spherical caps above and below the latitude circle we give detailed analysis of these convergence and transition layer behaviors