Nonlinear stability of rarefaction waves for the Boltzmann equation

DOI10.1007/s00205-005-0414-1zbMath1095.76024OpenAlexW2048456913MaRDI QIDQ2498087

Huijiang Zhao, Tong Yang, Shih-Hsien Yu, Tai-Ping Liu

Publication date: 11 August 2006

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-005-0414-1

zbMATH Keywords

energy methodviscous conservation laws\(H\)-theorem

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Interfacial stability and instability in hydrodynamic stability (76E17)

Related Items

The Boltzmann equation with frictional force, Large-time behavior for fluid and kinetic plasmas with collisions, Stability of the Boltzmann equation with potential forces on torus, The Lp-regularity properties of nonlocal wave equations and applications, Large time behavior of the solutions to the Boltzmann equation with specular reflective boundary condition, Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system with given magnetic field, Stability of contact discontinuity for the Boltzmann equation, Cauchy problem for the Vlasov-Poisson-Boltzmann system, Asymptotics toward viscous contact waves for solutions of the Landau equation, The 3D Vlasov-Poisson-Landau system near 1D local Maxwellians, On the cutoff approximation for the Boltzmann equation with long-range interaction, Stability of rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann system with hard potentials, The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball. III: The 3-D Boltzmann equation, Stability of the Rarefaction Wave of the Vlasov--Poisson--Boltzmann System, Kinetic Theory and Gas Dynamics, Some Historical Perspectives, Stability of a superposition of shock waves with contact discontinuities for the Jin-Xin relaxation system, Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation, Compressible Euler–Maxwell limit for global smooth solutions to the Vlasov–Maxwell–Boltzmann system, Long time behavior of the Fokker-Planck-Boltzmann equation, Stability of rarefaction waves for the non-cutoff Vlasov-Poisson-Boltzmann system with physical boundary, The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture, Small Knudsen rate of convergence to contact wave for the Landau equation, Stability of planar rarefaction wave to the 3D bipolar Vlasov–Poisson–Boltzmann system, Convergence rate to stationary solutions for Boltzmann equation with external force, Stability of nonlinear wave patterns to the bipolar Vlasov-Poisson-Boltzmann system, Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System, Compressible Navier-Stokes approximation to the Boltzmann equation, Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations, The specular reflective boundary problem for the Boltzmann equation with soft potentials, Nonlinear hyperbolic waves in relativistic gases of massive particles with Synge energy, On the Cauchy problem for the Boltzmann equation in the whole space: Global existence and uniform stability in \(L_{\xi}^{2}(H_{x}^{N})\), Behaviour of the Fokker-Planck-Boltzmann equation near a Maxwellian, Long time behavior of the Fokker-Planck-Boltzmann equation with soft potential, Contact discontinuity with general perturbations for gas motions, Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains, Stability of rarefaction waves of the Navier-Stokes-Poisson system, Global existence and full regularity of the Boltzmann equation without angular cutoff, Hydrodynamic limit of the Boltzmann equation with contact discontinuities, Convergence to rarefaction waves for the nonlinear Boltzmann equation and compressible Navier-Stokes equations, The Boltzmann equation with soft potentials near a local Maxwellian, Small Knudsen rate of convergence to rarefaction wave for the Landau equation, Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system, The Vlasov-Poisson-Landau system near a local Maxwellian, Stability of contact discontinuity for the two-species Vlasov–Poisson–Boltzmann system, Thermal creep flow for the Boltzmann equation, Justification of limit for the Boltzmann equation related to Korteweg theory, Stability of rarefaction wave for a macroscopic model derived from the Vlasov-Maxwell-Boltzmann system, Fluid dynamic limit to rarefaction wave for the Boltzmann equation, Stability of rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann system, Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation, Global existence and decay of solutions for soft potentials to the Fokker-Planck-Boltzmann equation without cut-off, The regularity properties and blow-up of solutions for nonlocal wave equations and applications, Stability of rarefaction wave for viscous vasculogenesis model, The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent transport coefficients, A half-space problem for the Boltzmann equation with specular reflection boundary condition, Stability of Superposition of Two Viscous Shock Waves for the Boltzmann Equation, Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition, On the Cauchy problem of Boltzmann equation with a very soft potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
• Energy method for Boltzmann equation
• Shock profile solutions of the Boltzmann equation
• Nonlinear asymptotic stability of viscous shock profiles for conservation laws
• On a boundary layer problem for the nonlinear Boltzmann equation
• On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
• The Boltzmann equation and its applications
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• The mathematical theory of dilute gases
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• On the Milne problem and the hydrodynamic limit for a steady Boltzmann equation model
• Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations
• Sur la théorie de l'équation intégrodifferentielle de Boltzmann
• Kinetic theory and fluid dynamics
• Hyperbolic systems of conservation laws II
• On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas
• The milne and kramers problems for the boltzmann equation of a hard sphere gas
• On the initial layer and the existence theorem for the nonlinear Boltzmann equation
• A classification of well-posed kinetic layer problems
• Asymptotics toward rarefaction wave of solutions of the Broadwell model of a discrete velocity gas
• The fluid dynamic limit of the nonlinear boltzmann equation
• THE CLASSICAL INCOMPRESSIBLE NAVIER-STOKES LIMIT OF THE BOLTZMANN EQUATION
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Linear and nonlinear large-time behavior of solutions of general systems of hyperbolic conservation laws
• Hydrodynamic limits with shock waves of the Boltzmann equation
• Nonlinear Stability of Strong Rarefaction Waves for Compressible Navier--Stokes Equations
• The Boltzmann equation in the whole space