on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

categories isomorphic to fns the main result in this paper is that the category of fuzzy neighborhood spaces is isomorphic to that of fuzzifying topological spaces

analytic results related to magneto hydrodynamic turbulence abstract analytic results are provided for topics related to the magneto hydrodynamic turbulence scaling exponents of general structure functions geometric criteria for singularity formation and dissipative solutions

on fuzzy pseudo metric spaces this paper attempts to endow the fuzzy pseudo metric in the sense of george and veeramani with many valued topological structures it is shown that george and veeramani s fuzzy pseudo metric can be characterized by a family of compatible ordinary pseudo metrics called pseudo metric chain in this paper then two kinds of many valued topological structures fuzzifying topology and fuzzifying uniformity are generated by this fuzzy pseudo metric and their properties are also investigated

local regularity criteria of the 3d navier stokes and related equations abstract in this paper we are concerned with the local regularity of suitable weak solutions to the 3d navier stokes equations and its generalized case with fractional power of the laplacian 3 4 1 in the first part we derive some regularity criteria in terms of the deformation tensor d u for the classical navier stokes equations in the second part for the fractional case we obtain some regularity conditions for suitable weak solutions including the velocity u the gradient of the velocity u the rotation tensor u and the deformation tensor d u this generalizes the results obtained by gustafson et al 2007

fuzzy pseudometric spaces vs fuzzifying structures in this paper we apply the representation theorem established in mardones perez and de prada vicente 2012 12 to define and study the degree in which some topological type properties of fuzzy pseudometric spaces are fulfilled fuzzifying structures which appear naturally are also investigated and the relation between these structures and fuzzy pseudometric spaces is explored

a new car following model considering the related factors of a gyroidal road abstract a novel car following model was proposed to describe the motion of the vehicles on a single lane gyroidal road we explore the related effects of gyroidal road upon uniform traffic flow analytically and numerically the analytical result shows that the related factors of gyroidal road including the friction coefficient radius of curvature and slope have great influences on the stability of the uniform flow respectively the modified kdv korteweg de vries equation is derived in the unstable area and the kink solution is obtained near the critical point a series of simulations are conducted to verify the effects upon uniform traffic flow under different road conditions it is shown that the amplitudes of the headway oscillation wave were affected by the friction coefficient radius of curvature and slope respectively the numerical results are in good agreement with the analytical results

a novel lattice hydrodynamic model accounting for driver s memory effect and the difference of optimal velocity on curved road abstract a novel lattice hydrodynamic model is put forward which takes the effects of driver s memory and difference of optimal velocity into account on curved road linear stability analysis for the novel model is discussed and the stability condition is deduced through nonlinear analysis the mkdv equation is deduced to explore the evolution of jams near the vertex the exact solution of the mkdv equation is also derived the influence of the above two factors on traffic stability are investigated by numerical examples both numerical and analytical results demonstrate that memory effect and the difference of optimal velocity on curved road can ease traffic jams efficiently

kdv and kink antikink solitons in car following models abstract the jams in the congested traffic are related with various density waves which might be governed by the nonlinear wave equations such as the korteweg de vries kdv equation the burgers equation and the modified korteweg de vries mkdv equation three different versions of optimal velocity models are examined the stability conditions of the models are obtained by using the linear stability theory the kdv equation near the neutral stability line and the mkdv equation around the critical point are derived by applying the reductive perturbation method respectively the traffic jams could be thus described by the kdv and kink antikink soliton solutions for the two kinds of equations the general solutions are given for which can lead to specific solutions in previous work moreover they are applied to solve a new model the full velocity difference model and the corresponding kdv and kink antikink soliton solutions could be quickly obtained which demonstrates the general solutions presented herein are useful

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

a representation theorem for fuzzy pseudometrics in this paper we show that there exists a one to one correspondence between a certain class of fuzzy pseudometrics in the sense of kramosil and michalek and 0 1 indexed families of ordinary pseudometrics satisfying a property of lower semicontinuity the aforementioned bijection is proved to be independent of the t norm and it provides a representation theorem for a large class of fuzzy pseudometric spaces further the relations between the uniformities and topologies both generated by the fuzzy pseudometric and by the corresponding family of ordinary pseudometrics are also investigated

analysis of social optimum for staggered shifts in a single entry traffic corridor with no late arrivals abstract this paper investigates the traffic flow dynamics under the social optimum so principle in a single entry traffic corridor with staggered shifts from the analytical and numerical perspectives the lwr lighthill whitham and richards model and the greenshield s velocity density function are utilized to describe the dynamic properties of traffic flow the closed form so solution is analytically derived and some numerical examples are used to further testify the analytical solution the optimum proportion of the numbers of commuters with different desired arrival times is further discussed where the analytical and numerical results both indicate that the cumulative outflow curve under the so principle is piecewise smooth

asymptotic solutions for a multi anticipative car following model abstract using a long wave expansion we study the asymptotic solutions near a critical point of a multi anticipative car following model a suitable rescaling of the variables then yields a modified korteweg de vries mkdv equation with higher order corrections an equation of this general form has already been investigated in detail in case of a simple model which allows us to use these results we are thus led to the conclusion that the characteristic features of the multi interaction model in the congested state can be obtained from the simple model by appropriately scaling the results

an asymmetric full velocity difference car following model abstract this paper presents a car following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream the problems of the prevalent general force gf model and the full velocity difference fvd model were solved furthermore the optimal velocity ov model the gf model and the fvd model are proved to be the special cases of the proposed asymmetric full velocity difference afvd model the mathematical model is presented followed by simulation analysis which demonstrates the properties of the afvd model

axisymmetric solutions to the 3d euler equations abstract here we consider the 3 d incompressible euler equations with axisymmetric velocity without swirl first we will show that if u 0 c s l 2 s 1 and 0 x c x 1 2 x 2 2 then there exists a unique u c 0 c s that solves the equation this conclusion improves on the related results given by majda a l bertozzi a majda vorticity and incompressible flow in cambridge texts in applied mathematics vol 27 2002 a majda vorticity and the mathematical theory of incompressible fluid flow comm pure appl math 39 1986 s187 s220 and by raymond x saint raymond remarks on axisymmetric solutions of the incompressible euler system comm partial differential equations 19 1994 321 334 on the other hand if u 0 l 2 0 l and 0 x 1 2 x 2 2 l then there exists a unique quasilipschitzian solution u c 0 c 1 this improves on the corresponding results due to raymond x saint raymond remarks on axisymmetric solutions of the incompressible euler system comm partial differential equations 19 1994 321 334 and to chae and kim d chae n kim axisymmetric weak solutions of the 3 d euler equations for incompressible fluid flows nonlinear anal 29 12 1997 1393 1404

symmetric nonbarotropic flows with large data and forces we prove the global existence of weak solutions of the navier stokes equations of compressible nonbarotropic flow in three space dimensions with initial data and external forces which are large discontinuous and spherically or cylindrically symmetric the analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry and the equations hold in the sense of distributions in the set where the density is positive in addition the mass and momentum equations hold weakly in the entire space time domain but with a nonstandard interpretation of the viscosity terms as distributions solutions are obtained as limits of solutions in annular regions between two balls or cylinders and the analysis allows for the possibility that energy is absorbed into the origin or axis and is lost in the limit as the inner radius goes to zero

parabolic equations with vmo coefficients in sobolev spaces with mixed norms an lq lp theory of divergence and non divergence form parabolic equations is presented the main coefficients are supposed to belong to the class vmox which in particular contains all measurable functions depending only on t the method of proving simplifies the methods previously used in the case p q

a regularity criterion for the weak solutions to the navier stokes fourier system we show that any weak solution to the full navier stokes fourier system emanating from the data belonging to the sobolev space w 3 2 remains regular as long as the velocity gradient is bounded the proof is based on the weak strong uniqueness property and parabolic a priori estimates for the local strong solutions

fuzzifying uniform spaces abstract we introduce the concept of fuzzifying uniform spaces in the framework of fuzzifying topology and establish some fundamental properties of fuzzifying uniform spaces

dynamics of singularity surfaces for compressible viscous flows in two space dimensions we prove the global existence of solutions of the navier stokes equations of compressible barotropic flow in two space dimensions which exhibit convecting singularity curves the fluid density and velocity gradient have jump discontinuities across these curves exactly as predicted by the rankine hugoniot conditions and these jump discontinuities decay exponentially in time more rapidly for smaller viscosities the singularity curves remain c1 despite the fact that the velocity fields which convect them are not continuously differentiable 2002 wiley periodicals inc

combined effects of drivers disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability analytical studies abstract driver s disturbance risk preference is defined as the driver s reaction degree to the disturbance which is a kind of the driver s attributes and can be expressed by the disturbance risk preference coefficient this paper proposes a new car following model and firstly attempts to analytically investigate the combined effects of drivers disturbance risk preference heterogeneity and the nearest following vehicle headway on traffic flow instability under some specific traffic scenarios solution of the model yields many insights including the following 1 when drivers disturbance risk preference increases from the following driver to the preceding driver traffic flow instability increases and the bigger the disturbance risk preference coefficient ratio of the preceding driver s coefficient to the following driver s coefficient the bigger the increasing effect and vice versa at this scenario the nearest following vehicle headway increases traffic flow instability 2 when drivers disturbance risk preference is homogeneous drivers disturbance risk preference and the nearest following vehicle headway have no effects on traffic flow instability 3 when drivers disturbance risk preference reduces from the following driver to the preceding driver for the general traffic situation traffic flow instability reduces and the smaller the disturbance risk preference coefficient ratio of the preceding driver s coefficient to the following driver s coefficient the bigger the reducing effect and vice versa at this scenario if the coefficient ratio reduces from the following to the preceding or is homogeneous the nearest following vehicle headway increases traffic flow instability otherwise the effects of the nearest following vehicle headway on traffic flow instability cannot be confirmed

an application of a representation theorem for fuzzy metrics to domain theory in this paper we study the interplay between fuzzy metric spaces and domain theory using the representation theorem established in mardones perez and de prada vicente 2012 12 we will prove that suitable restrictions of completeness in fuzzy metric spaces correspond to a structure of domain in the poset of formal balls endowed with appropriate orders

traffic behavior of mixed traffic flow with two kinds of different self stabilizing control vehicles abstract in this paper we propose a heterogeneous car following model in terms of an extension to the original optimal velocity model characterizing two classes of different self stabilizing control vehicles linear stability analysis method is utilized to the extended model for purpose to explore how the varying percentages of the vehicles with short duration self stabilizing control influence the stability of the heterogeneous traffic flow we obtain the neutral stability lines for different percentages of two classes of vehicles with finding that the traffic flow trends to stable with the decrease of the percentage for short duration self stabilizing control vehicles moreover we explore a special case that the same numbers of two different classes of vehicles with self stabilizing control we theoretically derive the stability condition of the special case and conclude the effect of the average value and the standard deviation of two time gaps on the heterogeneous traffic stability at last direct simulations are conducted to verify the conclusion of theoretical analysis

navier stokes equations for compressible fluids global existence and qualitative properties of the solutions in the general case we consider the equations which describe the motion of a viscous compressible fluid taking into consideration the case of inflow and or outflow through the boundary by means of some a priori estimates we prove the existence of a global in time solution moreover as a consequence of a stability result we show that there exist a periodic solution and a stationary solution

a beale kato majda criterion for three dimensional compressible viscous heat conductive flows we prove a blow up criterion in terms of the upper bound of 1 for a strong solution to three dimensional compressible viscous heat conductive flows the main ingredient of the proof is an a priori estimate for a quantity independently introduced in haspot regularity of weak solutions of the compressible isentropic navier stokes equation arxiv 1001 1581 2010 and sun et al j math pure appl 95 36 47 2011 whose divergence can be viewed as the effective viscous flux

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

a new approach for fuzzy topology ii abstract we point out a new approach for fuzzy topology with fuzzy logic and discuss the neighborhood structure of a point and the convergence of nets and filters in this new framework

stabilization effect of traffic flow in an extended car following model based on an intelligent transportation system application an extended car following model is proposed by incorporating an intelligent transportation system in traffic the stability condition of this model is obtained by using the linear stability theory the results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by applying the reductive perturbation method the traffic jam could be thus described by the kink antikink soliton solution for the mkdv equation from the simulation of space time evolution of the vehicle headway it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front and the analytical result is consonant with the simulation one

the relationship between a fuzzy uniformity and its family of a level uniformities abstract we show that a fuzzy uniformity d is uniquely determined by its family of level uniformities d 0 1 on the other hand if a family d 0 1 of uniformities on a set x is given and the family satisfies certain conditions then there exists a unique fuzzy uniformity d on x whose family of level uniformities is the given family

friction coefficient and radius of curvature effects upon traffic flow on a curved road abstract we investigate the friction coefficient and radius of curvature effects upon traffic flow analytically and numerically a new model is proposed to describe the motion of vehicles running on a curved road the stability condition is obtained by the use of control theories the nonlinear analysis method is taken to derive the modified kdv korteweg de vries equation and the kink antikink solution is obtained near the critical point simulations are carried out to verify the double effects upon traffic flow the flux increases but the stability decreases with an increase of the two parameters numerical results are in good agreement with the analytical results

stabilization and enhancement of traffic flow by the next nearest neighbor interaction the car following model of traffic is extended to take into account the car interaction before the next car ahead the next nearest neighbor interaction the traffic behavior of the extended car following model is investigated numerically and analytically it is shown that the next nearest neighbor interaction stabilizes the traffic flow the jamming transition between the freely moving and jammed phases occurs at a higher density than the threshold of the original car following model by increasing the maximal velocity the traffic current is enhanced without jam by the stabilization effect the jamming transition is analyzed with the use of the linear stability and nonlinear perturbation methods the traffic jam is described by the kink solution of the modified korteweg char21 de vries equation the theoretical coexisting curve is in good agreement with the simulation result

stabilization analysis and modified korteweg de vries equation in a cooperative driving system two lattice traffic models are proposed by incorporating a cooperative driving system the lattice versions of the hydrodynamic model of traffic flow are described by the differential difference equation and difference difference equation respectively the stability conditions for the two models are obtained using the linear stability theory the results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system the modified korteweg de vries equation the mkdv equation for short near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink anti kink soliton solutions obtained from the mkdv equations

nonlinear analysis for a modified continuum model considering electronic throttle et and backward looking effect abstract in this research a new car following model is developed by considering the influences of electronic throttle et dynamics and backward looking effect the improved car following model is transformed into a new continuum model through the relationship between the microscopic variables and macroscopic variables the linear stability condition of the extended continuum model can be obtained according to the linear stability theory the neutral stability curve shows that backward looking effect will improve the stability of traffic flow the kdv burgers equation is derived by the nonlinear analysis which can be used to describe the spreading behavior of traffic flow density wave in traffic congestion nearby the neutral stability line numerical experiments have been carried out including the shock waves rarefaction waves and energy consumption the numerical simulation results indicate that the traffic flow stability can be enhanced by considering et dynamics and backward looking effect in addition the above two factors can also effectively reduce energy consumption

regularity and singularity in solutions of the three dimensional navier stokes equations higher moments of the vorticity field m t in the form of l 2 m norms graphic 1 are used to explore the regularity problem for solutions of the three dimensional incompressible navier stokes equations on the domain graphic 2 it is found that the set of quantities formula 3 provide a natural scaling in the problem resulting in a bounded set of time averages d m t on a finite interval of time 0 t the behaviour of d m 1 d m is studied on what are called good and bad intervals of 0 t which are interspersed with junction points neutral i for large but finite values of m with large initial data m 0 o gr 4 it is found that there is an upper bound formula 4 which is punctured by infinitesimal gaps or windows in the vertical walls between the good bad intervals through which solutions may escape while this result is consistent with that of leray leray 1934 acta math 63 193 248 doi 10 1007 bf02547354 5 and scheffer scheffer 1976 pacific j math 66 535 552 this estimate for m corresponds to a length scale well below the validity of the navier stokes equations 1 embed inline graphic 1 gif 2 embed inline graphic 2 gif 3 embed graphic 1 gif 4 embed graphic 2 gif 5 http dx doi org doi 10 1007 bf02547354

fuzzifying topology induced by a strong fuzzy metric a construction of a fuzzifying topology induced by a strong fuzzy metric is presented properties of this fuzzifying topology in particular its convergence structure are studied our special interest is in the study of the relations between products of fuzzy metrics and the products of the induced fuzzifying topologies

nonlinear analysis of traffic flow on a gradient highway abstract we investigate the slope effects upon traffic flow on a single lane gradient uphill downhill highway analytically and numerically the stability condition neutral stability condition and instability condition are obtained by the use of linear stability theory it is found that stability of traffic flow on the gradient varies with the slopes the burgers korteweg de vries kdv and modified korteweg de vries mkdv equations are derived to describe the triangular shock waves soliton waves and kink antikink waves in the stable meta stable and unstable region respectively a series of simulations are carried out to reproduce the triangular shock waves kink antikink waves and soliton waves results show that amplitudes of the triangular shock waves and kink antikink waves vary with the slopes the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance moreover both the kink antikink waves and the solitary waves propagate backwards the numerical simulation shows a good agreement with the analytical result

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

global weak solution and blow up criterion of the general ericksen leslie system for nematic liquid crystal flows abstract in this paper we investigate the three dimensional general ericksen leslie e l system with ginzburg landau type approximation modeling nematic liquid crystal flows first by overcoming the difficulties from lack of maximum principle for the director equation and high order nonlinearities for the stress tensor we prove existence of global in time weak solutions under physically meaningful boundary conditions and suitable assumptions on the leslie coefficients which ensures that the total energy of the e l system is dissipated moreover for the e l system with periodic boundary conditions we prove the local well posedness of classical solutions under the so called parodi s relation and establish a blow up criterion in terms of the temporal integral of both the maximum norm of the curl of the velocity field and the maximum norm of the gradient of the liquid crystal director field

remarks on the regularity criteria of generalized mhd and navier stokes systems we study the regularity criteria of the three dimensional generalized magnetohydrodynamics mhd and navier stokes systems in particular we show that the regularity criteria of the generalized mhd system may be reduced to depend only on two diagonal entries of the jacobian matrix of the velocity vector field or one vorticity component and one entry of the jacobian matrix of the velocity vector field

existence for non isothermal fluid flows with tresca s friction and cattaneo s heat law abstract we consider a two dimensional non isothermal incompressible fluid flow involving heat transfer and friction the problem is described by the non stationary navier stokes system and by the hyperbolic heat equation derived from cattaneo s heat flux law which allows to overcome the paradox of infinite propagation speed we assume a strong coupling due to temperature dependent viscosity and velocity dependent heat capacity moreover we consider tresca s friction boundary conditions for the flow we prove an existence result for this problem by using a fixed point technique

intermittency and regularity issues in 3d navier stokes turbulence two related open problems in the theory of 3d navier stokes turbulence are discussed in this paper the first is the phenomenon of intermittency in the dissipation field dissipation range intermittency was first discovered experimentally by batchelor and townsend over fifty years ago it is characterized by spatio temporal binary behaviour in which long quiescent periods in the velocity signal are interrupted by short active events during which there are violent fluctuations away from the average the second and related problem is whether solutions of the 3d navier stokes equations develop finite time singularities during these events this paper shows that leray s weak solutions of the three dimensional incompressible navier stokes equations can have a binary character in time the time axis is split into good and bad intervals on the good intervals solutions are bounded and regular whereas singularities are still possible within the bad intervals an estimate for the width of the latter is very small and decreases with increasing reynolds number it also decreases relative to the lengths of the good intervals as the reynolds number increases within these bad intervals lower bounds on the local energy dissipation rate and other quantities such as u t and u t are very large resulting in strong dynamics at sub kolmogorov scales intersections of bad intervals for n 1 are related to the potentially singular set in time it is also proved that the navier stokes equations are conditionally regular provided in a given bad interval the energy has a lower bound that is decaying exponentially in time

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

on fuzzy uniformities induced by a fuzzy metric space abstract different types of fuzzy uniformities have been introduced in the literature standing out the notions due to hutton hohle and lowen the main purpose of this paper is to study several methods to endow a fuzzy metric space x m in the sense of george and veeramani with a probabilistic uniformity and with a hutton 0 1 quasi uniformity we will show the functorial behavior of these constructions as well as its relation with respect to lowen s functors and katsaras s functors which establish a relationship between the categories of probabilistic uniformities and hutton 0 1 quasi uniformities with the category of classical uniformities respectively furthermore we also study the fuzzy topologies associated with these fuzzy uniformities

lagrangean structure and propagation of singularities in multidimensional compressible flow we study the propagation of singularities in solutions of the navier stokes equations of compressible barotropic fluid flow in two and three space dimensions the solutions considered are in a fairly broad regularity class for which initial densities are nonnegative and essentially bounded initial energies are small and initial velocities are in certain fractional sobolev spaces we show that if the initial density is bounded below away from zero in an open set v then each point of v determines a unique integral curve of the velocity field and that this system of integral curves defines a locally bi holder homeomorphism of v onto its image at each positive time this lagrangean structure is then applied to show that if the initial density has a limit at a point of such a set v from a given side of a continuous hypersurface in v then at each later time both the density and the divergence of the velocity have limits at the transported point from the corresponding side of the transported hypersurface which is also a continuous manifold if the limits from both sides exist then the rankine hugoniot conditions hold in a strict pointwise sense showing that the jump in the divergence of the velocity is proportional to the jump in the pressure this leads to a derivation of an explicit representation for the strength of the jump in the logarithm of the density from which it follows that discontinuities persist for all time convecting along fluid particle paths and in the case that the pressure is strictly increasing in density having strengths which decay exponentially in time

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

nonlinear analysis for a modified continuum model considering driver s memory and backward looking effect abstract account for the integral form of optimal velocity changes with memory and backward looking effect an extended car following model is proposed in this paper through the relation between macro and micro variables the extended car following is transformed to a new continuum model according to the linear stability theory the linear stability s condition of the presented model is obtained the modified kdv burgers equation is established through non linear analysis to describe the spreading behavior of the traffic density wave near the neutral stability line the numerical simulation results show that the backward looking effect can improve the traffic flow s stability and the integral form of optimal velocity changes with memory can relieve the traffic congestion

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

traffic bottleneck characteristics caused by the reduction of lanes in an optimal velocity model abstract in this paper the lane reduction bottleneck is investigated using the optimal velocity model in which two kinds of vehicles fast and slow are introduced the asymmetric lane changing rules in the slowdown section and the lane squeezing behaviors at the bottleneck are taken into account under the periodic boundary condition the numerical simulations are performed the traffic states change with increasing density and an interesting phenomenon of ratio inversion appears when the current saturates the headway and velocity discontinuously vary with the position in addition traffic patterns and the phase transition points depend greatly on the speed limit and the length of the slowdown section

effect of looking backward on traffic flow in an extended multiple car following model abstract in this paper a new car following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow and the neutral stability condition of this model can be obtained by using the linear stability theory numerical simulation shows that the proposed model is theoretically an improvement over previous ones

on approximate solutions of the incompressible euler and navier stokes equations abstract we consider the incompressible euler or navier stokes ns equations on a torus t d in the functional setting of the sobolev spaces h 0 n t d of divergence free zero mean vector fields on t d for n d 2 1 we present a general theory of approximate solutions for the euler ns cauchy problem this allows to infer a lower bound t c on the time of existence of the exact solution u analyzing a posteriori any approximate solution u a and also to construct a function n such that u t u a t n n t for all t 0 t c both t c and n are determined solving suitable control inequalities depending on the error of u a the fully quantitative implementation of this scheme depends on some previous estimates of ours on the euler ns quadratic nonlinearity morosi and pizzocchero 2010 in press 7 8 to keep in touch with the existing literature on the subject our results are compared with a setting for approximate euler ns solutions proposed in chernyshenko et al 2007 1 as a first application of the present framework we consider the galerkin approximate solutions of the euler ns cauchy problem with a specific initial datum considered in behr et al 2001 9 in this case our methods allow amongst else to prove global existence for the ns cauchy problem when the viscosity is above an explicitly given bound