From Discrete Velocity Boltzmann Equations to Gas Dynamics Before Shocks

This article is devoted to the proof of the hydrodynamic limit for a discrete velocity Boltzmann equation before appearance of shocks in the limit system.

[1]  R. Illner,et al.  Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory , 1988 .

[2]  H. Reinhard,et al.  Equations aux dérivées partielles , 1987 .

[3]  L. Saint-Raymond,et al.  Convergence of Solutions to the Boltzmann Equation in the Incompressible Euler Limit , 2003 .

[4]  Eestence Globale à Donné de Cauchy Petites pour les modéles discrets de ―équation de Boltzmann , 1991 .

[5]  Y. Brenier,et al.  convergence of the vlasov-poisson system to the incompressible euler equations , 2000 .

[6]  Shi-Hsien Yu,et al.  Hydrodynamic limits with shock waves of the Boltzmann equation , 2005 .

[7]  François Bouchut,et al.  Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy , 2002 .

[8]  Cédric Villani,et al.  Cercignani's Conjecture is Sometimes True and Always Almost True , 2003 .

[9]  Large-time behavior of discrete velocity boltzmann equations , 1986 .

[10]  J. Bony Solutions globales bornées pour les modèles discrets de l'équation de Boltzmann en dimension $1$ d'espace , 1987 .

[11]  R. J. Diperna Uniqueness of Solutions to Hyperbolic Conservation Laws. , 1978 .

[12]  Athanasios E. Tzavaras,et al.  RELATIVE ENTROPY IN HYPERBOLIC RELAXATION , 2005 .

[13]  Kiyoshi Asano,et al.  The Euler limit and initial layer of the nonlinear Boltzmann equation , 1983 .

[14]  A. Tzavaras,et al.  Lyapunov Functionals and L1-Stability for Discrete Velocity Boltzmann Equations , 2003 .

[15]  Stefano Bianchini,et al.  Hyperbolic limit of the Jin‐Xin relaxation model , 2006 .

[16]  François Bouchut,et al.  Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics , 2002 .

[17]  François Golse,et al.  The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels , 2004 .

[18]  M. Feldman,et al.  Nonlinear Functionals of Multi-D Discrete Velocity Boltzmann Equations , 2004 .

[19]  G. Papanicolaou,et al.  The fluid‐dynamical limit of a nonlinear model boltzmann equation , 1979 .

[20]  Athanasios E. Tzavaras,et al.  Materials with Internal Variables and Relaxation to Conservation Laws , 1999 .

[21]  Benjamin Jourdain,et al.  Long-Time Asymptotics of a Multiscale Model for Polymeric Fluid Flows , 2006 .

[22]  Juan Soler,et al.  Multidimensional high-field limit of the electrostatic Vlasov-Poisson-Fokker-Planck system. , 2005 .

[23]  Alexis Vasseur,et al.  From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks , 2005, SIAM J. Math. Anal..

[24]  S. Varadhan,et al.  Hydrodynamical limit for a Hamiltonian system with weak noise , 1993 .

[25]  S. Kawashima Large-time behavior of solutions of the discrete Boltzmann equation , 1987 .

[26]  Athanasios E. Tzavaras,et al.  Structural Properties of Stress Relaxation and Convergence from Viscoelasticity to Polyconvex Elastodynamics , 2006 .

[27]  C. Dafermos The second law of thermodynamics and stability , 1979 .

[28]  H. Cabannes,et al.  The Discrete Boltzmann Equation (Theory and Applications) , 2022 .

[29]  Horng-Tzer Yau,et al.  Relative entropy and hydrodynamics of Ginzburg-Landau models , 1991 .

[30]  D. Serre Relaxations semi-linaire et cintique des systmes de lois de conservation , 2000 .

[31]  Yann Brenier,et al.  On a relaxation approximation of the incompressible Navier-Stokes equations , 2003 .

[32]  Abdelghani Bellouquid ON THE ASYMPTOTIC ANALYSIS OF KINETIC MODELS TOWARDS THE COMPRESSIBLE EULER AND ACOUSTIC EQUATIONS , 2004 .