From discrete velocity Boltzmann equations to gas dynamics before shocks

DOI10.1007/s10955-009-9709-1zbMath1168.82322OpenAlexW2094923258MaRDI QIDQ2391035

Alexis F. Vasseur, Florent Berthelin, Athanassios E. Tzavaras

Publication date: 24 July 2009

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-009-9709-1

zbMATH Keywords

hydrodynamic limitentropy methodsgas dynamicsdiscrete Boltzmann equations

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Statistical mechanics of plasmas (82D10) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (19)

Asymptotic analysis of Vlasov-type equations under strong local alignment regime ⋮ Criteria on contractions for entropic discontinuities of systems of conservation laws ⋮ The Inviscid Limit to a Contact Discontinuity for the Compressible Navier--Stokes--Fourier System Using the Relative Entropy Method ⋮ \(L^2\)-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws ⋮ On the convergence of the regularized entropy-based moment method for kinetic equations ⋮ Stability and Uniqueness for Piecewise Smooth Solutions to a Nonlocal Scalar Conservation Law with Applications to Burgers--Hilbert Equation ⋮ Finite time stability for the Riemann problem with extremal shocks for a large class of hyperbolic systems ⋮ Asymptotic limit to shocks for scalar balance laws using relative entropy ⋮ \(L^2\)-type contraction for systems of conservation laws ⋮ \(L^{2}\)-contraction for shock waves of scalar viscous conservation laws ⋮ An integral representation of functions in gas-kinetic models ⋮ Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-\(BV\) perturbations ⋮ \(L ^{2}\) stability estimates for shock solutions of scalar conservation laws using the relative entropy method ⋮ Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws ⋮ On uniqueness of solutions to conservation laws verifying a single entropy condition ⋮ Relative entropy and L2 stability to a shock for scalar balance laws ⋮ Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method ⋮ Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method ⋮ A Hierarchy of Hybrid Numerical Methods for Multiscale Kinetic Equations

Cites Work

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• The Euler limit and initial layer of the nonlinear Boltzmann equation
• Large-time behavior of solutions of the discrete Boltzmann equation
• Large-time behavior of discrete velocity Boltzmann equations
• The second law of thermodynamics and stability
• Materials with internal variables and relaxation to conservation laws
• Hydrodynamical limit for a Hamiltonian system with weak noise
• Lyapunov functionals and \(L^1\)-stability for discrete velocity Boltzmann equations
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
• Convergence of solutions to the Boltzmann equation in the incompressible Euler limit
• Semi-linear and kinetic relaxation for systems of conservation laws
• Nonlinear functionals of multi-D discrete velocity Boltzmann equations
• Cercignani's conjecture is sometimes true and always almost true
• Relative entropy and hydrodynamics of Ginzburg-Landau models
• Multidimensional high-field limit of the electrostatic Vlasov-Poisson-Fokker-Planck system
• Structural properties of stress relaxation and convergence from viscoelasticity to polyconvex elastodynamics
• Long-time asymptotics of a multiscale model for polymeric fluid flows
• Relative entropy in hyperbolic relaxation
• Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy
• Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory
• The fluid-dynamical limit of a nonlinear model boltzmann equation
• Eestence Globale à Donné de Cauchy Petites pour les modéles discrets de ―équation de Boltzmann
• On a relaxation approximation of the incompressible Navier-Stokes equations
• Hydrodynamic limits with shock waves of the Boltzmann equation
• convergence of the vlasov-poisson system to the incompressible euler equations
• ON THE ASYMPTOTIC ANALYSIS OF KINETIC MODELS TOWARDS THE COMPRESSIBLE EULER AND ACOUSTIC EQUATIONS
• From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks
• Hyperbolic limit of the Jin‐Xin relaxation model

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