existence results for the flow of viscoelastic fluids with a differential constitutive law where 2 is the symmetric extra stress tensor the total stress is given by g pl i where p is the hydrodynamic pressure 4 is the rate of deformation tensor g u vu vu u being the velocity field a is the relaxation time a2 the retardation time 0 i a a1 and q is the fluid viscosity the symbol a d t denotes an objective frame indifferent derivative i 181 more precisely

on flows associated to sobolev vector fields in wiener spaces an approach a la diperna lions in this paper we extend the diperna lions theory of flows associated to sobolev vector fields to the case of cameron martin valued vector fields in wiener spaces e having a sobolev regularity the proof is based on the analysis of the continuity equation in e and on uniform gaussian commutator estimates in finite dimensional spaces

diophantine geometry over groups viii stability this paper is the eighth in a sequence on the structure of sets of solutions to systems of equations in free and hyperbolic groups projections of such sets diophantine sets and the structure of denable sets over free and hyperbolic groups in this eighth paper we use a modication of the sieve procedure which was used in proving quantier elimination in the theory of a free group to prove that free and torsion free gromov hyperbolic groups are stable in the

on a micro macro model for polymeric fluids near equilibrium in this paper we study a micro macro model for polymeric fluid the system involves coupling between the macroscopic momentum equation and a microscopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation we employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure for the initial data not far from the equilibrium we prove the global existence and uniqueness of classical solutions to the system 2006 wiley periodicals inc

convergence of numerical approximations to non linear continuity equations with rough force fields we prove quantitative regularity estimates for the solutions to non linear continuity equations and their discretized numerical approximations on cartesian grids when advected by a rough force field this allows us to not only recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes our proof is based on novel commutator estimates quantifying and extending to the non linear case the classical commutator approach of the theory of renormalized solutions

on the uniqueness of solutions to continuity equations abstract we obtain sufficient conditions for the uniqueness of solutions to the cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous

compactness for nonlinear continuity equations abstract we prove compactness and hence existence for solutions to a class of nonlinear transport equations the corresponding models combine the features of linear transport equations and scalar conservation laws we introduce a new method which gives quantitative compactness estimates compatible with both frameworks

local existence for the fene dumbbell model of polymeric fluids we study the well posedness of a multi scale model of polymeric fluids the microscopic model is the kinetic theory of the finitely extensible nonlinear elastic fene dumbbell model the macroscopic model is the incompressible non newton fluids with polymer stress computed via the kramers expression the boundary condition of the fene type fokker planck equation is proved to be unnecessary by the singularity on the boundary other main results are the local existence uniqueness and regularity theorems for the fene model in certain parameter range

from the boltzmann equations to the equations of incompressible fluid mechanics i we consider here the problem of deriving rigorously from boltzmann s equation globally in time and for general initial conditions fluid mechanics equations such as the navier stokes or euler equations

the l2 decay for the 2d co rotation fene dumbbell model of polymeric flows abstract in this paper we mainly study the long time behavior of solutions to the finite extensible nonlinear elastic fene dumbbell model with dimension two in the co rotation case firstly we obtain the l 2 decay rate of the velocity of the 2d co rotation fene model is 1 t 1 2 with small data then by virtue of the littlewood paley theory we can remove the small condition our obtained sharp result improves considerably the recent results in 8 14

global well posedness of the d d oldroyd b type models with fractional laplacian dissipation abstract this paper focuses on the cauchy problem of the d dimensional incompressible oldroyd b type models for viscoelastic flow with fractional laplacian dissipation namely with 1 u and 2 for 1 1 2 d 4 2 0 and 1 2 1 d 2 we obtain the global regularity of strong solutions when the initial data u 0 0 are sufficiently smooth

on the lagrangian structure of transport equations the vlasov poisson system the vlasov poisson system is an important nonlinear transport equation used to describe the evolution of particles under their self consistent electric or gravitational field the existence of classical solutions is limited to dimensions d 3 under strong assumptions on the initial data whereas weak solutions are known to exist under milder conditions however in the setting of weak solutions it is unclear whether the eulerian description provided by the equation physically corresponds to a lagrangian evolution of the particles in this article we develop several general tools concerning the lagrangian structure of transport equations with nonsmooth vector fields and we apply these results to show that weak renormalized solutions of vlasov poisson are lagrangian and actually that the concepts of renormalized and lagrangian solutions are equivalent as a corollary we prove that finite energy solutions in dimension d 4 are transported by a global flow in particular they preserve all the natural casimir invariants and we obtain the global existence of weak solutions in any dimension under minimal assumptions on the initial data

mathematical existence results for the doi edwards polymer model in this paper we present some mathematical results on the doi edwards model describing the dynamics of flexible polymers in melts and concentrated solutions this model developed in the late 1970s has been used and extensively tested in modeling and simulation of polymer flows from a mathematical point of view the doi edwards model consists in a strong coupling between the navier stokes equations and a highly nonlinear constitutive law the aim of this article is to provide a rigorous proof of the well posedness of the doi edwards model namely that it has a unique regular solution we also prove which is generally much more difficult for flows of viscoelastic type that the solution is global in time in the two dimensional case without any restriction on the smallness of the data

le probleme de tchebychev pour le douzieme polynome cyclotomique let p n denote the largest prime factor of the integer n and 12 n n 4 n 2 1 we prove that for x large enough we have p x x 1 c with c 10 26531

steady nearly incompressible vector fields in two dimension chain rule and renormalization given bounded vector field b mathbb r d to mathbb r d scalar field u mathbb r d to mathbb r and a smooth function beta mathbb r to mathbb r we study the characterization of the distribution rm div beta u b in terms of div b and div ub in the case of bv vector fields b and under some further assumptions such characterization was obtained by l ambrosio c de lellis and j mal up to an error term which is a measure concentrated on the so called tangential set of b we answer some questions posed in their paper concerning the properties of this term in particular we construct a nearly incompressible bv vector field b and a bounded function u for which this term is nonzero for steady nearly incompressible vector fields b and under some further assumptions in the case when d 2 we provide complete characterization of div beta u b in terms of div b and div ub our approach relies on the structure of level sets of lipschitz functions on mathbb r 2 obtained by g alberti s bianchini and g crippa extending our technique we obtain new sufficient conditions when any bounded weak solution u of partial t u b cdot nabla u 0 is renormalized that is when it also solves partial t beta u b cdot nabla beta u 0 for any smooth function beta colon mathbb r to mathbb r as a consequence we obtain new a uniqueness result for this equation

the adaptive lagrangian particle method for macroscopic and micro macro computations of time dependent viscoelastic flows we propose a new numerical technique referred to as the adaptive lagrangian particle method alpm for computing time dependent viscoelastic flows using either a differential constitutive equation macroscopic approach or a kinetic theory model micro macro approach in alpm the eulerian finite element solution of the conservation equations is decoupled from the lagrangian computation of the extra stress at a number of discrete particles convected by the how in the macroscopic approach the extra stress carried by the particles is obtained by integrating the constitutive equation along the particle trajectories in the micro macro approach the extra stress is computed by solving along the particle paths the stochastic differential equation associated with the kinetic theory model at each time step alpm automatically enforces that all elements of the mesh have a number of lagrangian particles ranging within a user specified interval results are given for the start up flow between highly eccentric rotating cylinders using the fene and fene p dumbbell models for dilute polymer solutions c 1999 elsevier science s a all rights reserved

critical non sobolev regularity for continuity equations with rough velocity fields abstract we present a divergence free vector field in the sobolev space h 1 such that the flow associated to the field does not belong to any sobolev space the vector field is deterministic but constructed as the realization of a random field combining simple elements this construction illustrates the optimality of recent quantitative regularity estimates as it gives a straightforward example of a well posed flow which has nevertheless only very weak regularity

global wellposedness to the generalized oldroyd type models in r3 abstract it remains unknown whether smooth solutions of the 3d oldroyd models exist globally in viscoelastic fluids using the trick of transferring dissipation we get the global strong solutions of the generalized oldroyd models in three dimensions under the assumption that initial data is sufficiently small it improves the result in two dimensions obtained by elgndi and rousset 2015 4

on supersimple groups an infinite group with supersimple theory has a finite series of definable groups whose factors are infinite and either virtually fc or virtually simple modulo a finite fc centre a group which is type definable in a supersimple theory has a finite series of relatively definable groups whose factors are either abelian or simple groups in this decomposition the non abelian simple factors are unique up to isomorphism

boundary conditions for the microscopic fene models we consider the microscopic equation of finite extensible nonlinear elasticity fene models for polymeric fluids under a steady flow field it is shown that for the underlying fokker planck type of equations any preassigned distribution on the boundary will become redundant once the nondimensional number text it li frac hb k bt geq 2 where h is the elasticity constant sqrt b is the maximum dumbbell extension t is the temperature and k b is the usual boltzmann constant moreover if the probability density function is regular enough for its trace to be defined on the sphere m sqrt b then the trace is necessarily zero when text it li 2 these results are consistent with our numerical simulations as well as some recent well posedness results by preassuming a zero boundary distribution

well posedness for the fene dumbbell model of polymeric flows we prove local and global well posedness for the fene dumbbell model for a very general class of potentials indeed in prior local or global well posedness results conditions on the strength of the singularity or on the parameter b were made here we give a proof in the general case we also prove global existence results if the data is small or if we restrict to the co rotational model in dimension 2 2008 wiley periodicals inc

global existence and uniqueness result for the diffusive peterlin viscoelastic model abstract the aim of this paper is to present the existence and uniqueness result for the diffusive peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids the polymers are treated as two beads connected by a nonlinear spring the peterlin approximation of the spring force is used to derive the equation for the conformation tensor the latter is the time evolution equation with spatial diffusion of the conformation tensor using the energy estimates we prove global in time existence of a weak solution in two space dimensions we are also able to show the regularity and consequently the uniqueness of the weak solution

lagrangian flows and the one dimensional peano phenomenon for odes we consider the one dimensional ordinary differential equation with a vector field which is merely continuous and nonnegative and satisfies a condition on the amount of zeros although it is classically known that this problem lacks uniqueness of classical trajectories we show that there is uniqueness for the so called regular lagrangian flow by now usual notion of flow in nonsmooth situations as well as uniqueness of distributional solutions for the associated continuity equation the proof relies on a space reparametrization argument around the zeros of the vector field

un analogue du calcul de heegner on demontre les deux resultats suivants a si p est un nombre premier impair congru a 2 modulo 9 la courbe elliptique x 3 y 3 2pz 3 possede une infinite de points rationnels b si p est un nombre premier congru a 5 modulo 9 la courbe elliptique x 3 y 3 2p 2 z 3 possede une infinite de points rationnels

long time asymptotics of a multiscale model for polymeric fluid flows in this paper we investigate the long time behavior of some micro macro models for polymeric fluids hookean model and fene model in various settings shear flow general bounded domain with homogeneous dirichlet boundary conditions on the velocity general bounded domain with non homogeneous dirichlet boundary conditions on the velocity we use both probabilistic approaches coupling methods and analytic approaches entropy methods

blow up criterion for the incompressible viscoelastic flows abstract in this paper we are concerned with the incompressible viscoelastic flows in the periodic domain we establish a serrin type blow up criterion for 3 d periodic initial boundary problem which states a strong solution exists globally provided that the velocity satisfies serrin s condition and the l t l x norm of the deformation gradient are bounded we also establish blow up criterion in terms of the upper bound of the deformation gradient for 2 d periodic initial boundary problem the main ingredient of the proof is a priori estimate for an important quantity under the assumption that the deformation gradient is upper bounded whose divergence can be viewed as the effective viscous flux

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

sobolev estimates for solutions of the transport equation and ode flows associated to non lipschitz drifts it is known after jabin j differ equ 260 5 4739 4757 2016 and alberti et al ann pde 5 1 9 2019 that ode flows and solutions of the transport equation associated to sobolev vector fields do not propagate sobolev regularity even of fractional order in this paper we improve the result at clop and jylha j differ equ 266 8 4544 4567 2019 and show that some kind of propagation of sobolev regularity happens as soon as the gradient of the drift is exponentially integrable we provide sharp sobolev estimates and new examples as an application of our main theorem we generalize a regularity result for the 2d euler equation obtained by bahouri and chemin in bahouri and chemin arch ration mech anal 127 2 159 181 1994

continuity equations and ode flows with non smooth velocity in this paper we review many aspects of the well posedness theory for the cauchy problem for the continuity and transport equations and for the ordinary differential equation ode in this framework we deal with velocity fields that are not smooth but enjoy suitable weak differentiability assumptions we first explore the connection between the partial differential equation pde and the ode in a very general non smooth setting then we address the renormalization property for the pde and prove that such a property holds for sobolev velocity fields and for bounded variation velocity fields finally we present an approach to the ode theory based on quantitative estimates

existence of solution for a micro macro model of polymeric fluid the fene model abstract we analyse a non linear micro macro model of polymeric fluids in the case of a shear flow more precisely we consider the fene dumbbell model which models polymers by nonlinear springs accounting for the finite extensibility of the polymer chain we prove the existence of a unique solution to the stochastic differential equation which rules the evolution of a representative polymer in the flow and next deduce a local in time existence and uniqueness result on the system coupling the stochastic differential equation and the momentum equation on the fluid

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

global existence of weak solutions to the fene dumbbell model of polymeric flows systems coupling fluids and polymers are of great interest in many branches of sciences one of the most classical models to describe them is the fene finite extensible nonlinear elastic dumbbell model we prove global existence of weak solutions to the fene dumbbell model of polymeric flows the main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties the proof uses many weak convergence techniques in particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure in addition this quantity controls a rescaled defect measure of the gradient of the velocity

stochastic lagrangian particle approach to fractal navier stokes equations in this article we study the fractal navier stokes equations by using the stochastic lagrangian particle path approach in constantin and iyer comm pure appl math lxi 330 345 2008 more precisely a stochastic representation for the fractal navier stokes equations is given in terms of stochastic differential equations driven by levy processes based on this representation a self contained proof for the existence of a local unique solution for the fractal navier stokes equation with initial data in mathbb w 1 p is provided and in the case of two dimensions or large viscosity the existence of global solutions is also obtained in order to obtain the global existence in any dimensions for large viscosity the gradient estimates for levy processes with time dependent and discontinuous drifts are proved

global solutions of two dimensional incompressible viscoelastic flows with discontinuous initial data the global existence of weak solutions of the incompressible viscoelastic flows in two spatial dimensions has been a longstanding open problem and it is studied in this paper we show global existence if the initial deformation gradient is close to the identity matrix in l2 l and the initial velocity is small in l2 and bounded in lp for some p 2 while the assumption on the initial deformation gradient is automatically satisfied for the classical oldroyd b model the additional assumption on the initial velocity being bounded in lp for some p 2 may due to techniques we employed the smallness assumption on the l2 norm of the initial velocity is however natural for global well posedness one of the key observations in the paper is that the velocity and the effective viscous flux g are sufficiently regular for positive time the regularity of g leads to a new approach for the pointwise estimate for the deformation gradient without using l bounds on the velocity gradients in spatial variables 2015 wiley periodicals inc

continuity of velocity gradients in suspensions of rod like molecules we investigate the doi model for suspensions of rod like molecules in the dilute regime for certain parameter values the velocity gradient vs stress relation defined by the stationary and homogeneous flow is not rank one monotone we then consider the evolution of possibly large perturbations of stationary flows we prove that even in the absence of a microscopic cut off discontinuities in the velocity gradient cannot occur in finite time the proof relies on a novel type of estimate for the smoluchowski equation

global solutions for incompressible viscoelastic fluids we prove the existence of both local and global smooth solutions to the cauchy problem in the whole space and the periodic problem in the n dimensional torus for the incompressible viscoelastic system of oldroyd b type in the case of near equilibrium initial data the results hold in both two and three dimensional spaces the results and methods presented in this paper are also valid for a wide range of elastic complex fluids such as magnetohydrodynamics liquid crystals and mixture problems

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

prime values of a 2 p 4 a 2 p 4 we prove an asymptotic formula for the number of primes of the shape a 2 p 4 thereby refining the well known work of friedlander and iwaniec ann math 2 148 3 945 1040 1998 along the way we prove a result on equidistribution of primes up to x in which the moduli may be almost as large as x 2

global solutions to repulsive hookean elastodynamics the global existence of classical solutions to the three dimensional repulsive hookean elastodynamics around an equilibrium is considered by linearization and hodge s decomposition the compressible part of the velocity the density and the compressible part of the transpose of the deformation gradient satisfy klein gordon equations with speed sqrt 2 while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one the space time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence

on the representation of primes by cubic polynomials in two variables in an earlier paper see proc london math soc 3 84 2002 257 288 we showed that an irreducible integral binary cubic form f x y attains infinitely many prime values providing that it has no fixed prime divisor we now extend this result by showing that f m n still attains infinitely many prime values if m and n are restricted by arbitrary congruence conditions providing that there is still no fixed prime divisor two immediate consequences for the solvability of diagonal cubic diophantine equations are given

remarks on the blowup criteria for oldroyd models abstract we provide a new method to prove and improve the chemin masmoudi criterion for viscoelastic systems of oldroyd type in j y chemin n masmoudi about lifespan of regular solutions of equations related to viscoelastic fluids siam j math anal 33 1 2001 84 112 in two space dimensions our method is much easier than the one based on the well known losing a priori estimate and is expected to be easily adopted to other problems involving the losing a priori estimate

lagrangian solutions to the 2d euler system with l1 vorticity and infinite energy we consider solutions to the two dimensional incompressible euler system with only integrable vorticity thus with possibly locally infinite energy with such regularity we use the recently developed theory of lagrangian flows associated to vector fields with gradient given by a singular integral in order to define lagrangian solutions for which the vorticity is transported by the flow we prove strong stability of these solutions via strong convergence of the flow under the only assumption of l1 weak convergence of the initial vorticity the existence of lagrangian solutions to the euler system follows for arbitrary l1 vorticity relations with previously known notions of solutions are established

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

on the boltzmann equation for long range interactions we study the boltzmann equation without grad s angular cutoff assumption we introduce a suitable renormalized formulation that allows the cross section to be singular in both the angular and the relative velocity variables angular singularities occur as soon as one is interested in long range interactions while singularities in the relative velocity variable occur in the study of soft potentials in particular coulomb interaction together with several new estimates this new formulation enables us to prove existence of weak solutions and to give a proof of a conjecture by lions appearance of strong compactness under general fully realistic assumptions 2001 john wiley sons inc

on hydrodynamics of viscoelastic fluids in this paper we study a hydrodynamic system describing fluids with viscoelastic properties after a brief examination of the relations between several models we shall concentrate on a few analytical issues concerning them in particular we establish local existence and global existence with small initial data of classical solutions for an oldroyd system without an artificially postulated damping mechanism

estimates and regularity results for the diperna lions flow in this paper we derive new simple estimates for ordinary differential equations with sobolev coefficients these estimates not only allow to recover some old and recent results in a simple direct way but they also have some new interesting corollaries

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

well posedness for the dumbbell model of polymeric fluids the dumbbell model is a coupled hydrodynamic kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations we prove well posedness of this model by deriving directly a priori estimates on the stochastic model our results can be used to analyze stochastic simulation methods such as the ones that are based on brownian configuration fields

global solutions for micro macro models of polymeric fluids abstract we provide a new proof for the global well posedness of systems coupling fluids and polymers in two space dimensions compared to the well known existing method based on the losing a priori estimates our method is more direct and much simpler the co rotational fene dumbbell model and the coupling smoluchowski and navier stokes equations are studied as examples to illustrate our main ideas

global well posedness for 2d polymeric fluid models and growth estimate motivated by p constantin n masmoudi global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d comm math phys 278 2008 179 191 f lin ping zhang zhifei zhang on the global existence of smooth solution to the 2 d fene dumbbell model comm math phys 277 2008 531 553 we prove the global existence of smooth solutions to a coupled microscopic macroscopic model for polymeric fluid in 2d under the co rotational assumption furthermore we provide an estimate on the time growth of these solutions our method is general and can be applied to the co rotational fene model and to the rod like model without the co rotational assumption c 2008 elsevier b v all rights reserved

primes represented by binary cubic forms let f x y be a binary cubic form with integral rational coefficients and suppose that the polynomial f x y is irreducible in mathbb q x y and no prime divides all the coefficients of f we prove that the set f mathbb z 2 contains infinitely many primes unless f a b is even for each a b in mathbb z 2 in which case the set frac 1 2 f mathbb z 2 contains infinitely many primes 2000 mathematical subject classification primary 11n32 secondary 11n36 11r44

groups in supersimple and pseudofinite theories we consider groups g interpretable in a supersimple nite rank theory t such that t eq eliminates 9 1 it is shown that g has a denable soluble radical if g has rank 2 then if g is pseudonite it is soluble by nite and partial results are obtained under weaker hypotheses such as functional unimodularity of the theory a classication is obtained when t is pseudonite and g has a denable and denably

viscoelastic fluid models derived from kinetic equations for polymers differential relationships between velocity and stress are derived from the kinetic theory of polymeric liquids the fokker planck equation corresponding to the so called dumbbell theory for dilute solutions of polymers is considered achapman enskog expansion for time dependent nonhomogeneous flows is proposed when the elastic character of the fluid is small and the results included in the book of r bird c curtiss r armstrong and o hassager dynamics of polymeric liquids vol kinetic theory john wiley sons new york 1987 are recovered a comparison with oldroyd b fene and fene p fluids is presented in the frame of the plane couette flow

existence of global weak solutions to finitely extensible nonlinear bead spring chain models for dilute polymers with variable density and viscosity abstract we prove the existence of global in time weak solutions to a general class of coupled bead spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains with finitely extensible nonlinear elastic fene spring potentials the class of models under consideration involves the unsteady incompressible navier stokes equations with variable density and density dependent dynamic viscosity in a bounded domain in r d d 2 or 3 for the density the velocity and the pressure of the fluid with an elastic extra stress tensor appearing on the right hand side in the momentum equation the extra stress tensor stems from the random movement of the polymer chains and is defined by the kramers expression through the associated probability density function that satisfies a fokker planck type parabolic equation a crucial feature of which is the presence of a centre of mass diffusion term and a nonlinear density dependent drag coefficient we require no structural assumptions on the drag term in the fokker planck equation in particular the drag term need not be corotational with initial density 0 min max for the continuity equation where min 0 a square integrable and divergence free initial velocity datum u 0 for the navier stokes equation and a nonnegative initial probability density function 0 for the fokker planck equation which has finite relative entropy with respect to the maxwellian m associated with the spring potential in the model we prove via a limiting procedure on certain regularization parameters the existence of a global in time weak solution t t u t t to the coupled navier stokes fokker planck system satisfying the initial condition 0 u 0 0 0 u 0 0 such that t t min max t u t belongs to the classical leray space and t t has bounded relative entropy with respect to m and t t m has integrable fisher information w r t the gibbs measure d m q d q d x over any time interval 0 t t 0

global existence of weak solutions to two dimensional compressible viscoelastic flows abstract the global existence of weak solutions of the compressible viscoelastic flows in two spatial dimensions is studied in this paper we show the global existence if the initial velocity u 0 is small in h with an arbitrary 0 1 2 and the perturbation of 0 f 0 around the constant state 1 i are small in l 2 b p 1 2 p with p 1 1 16 2 4 one of the main ingredients is that the velocity and the effective viscous flux g i are sufficiently regular for positive time the regularity of g i helps to obtain the l estimate of density and deformation gradient and hence eliminates the possible concentration and oscillation issues