Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains

DOI10.1090/tran/8437zbMath1479.35661arXiv1806.09796OpenAlexW3165098735MaRDI QIDQ5158100

Renjun Duan, Shuangqian Liu

Publication date: 21 October 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.09796

zbMATH Keywords

Chapman-Enskog expansiondiffusive boundary conditioncompressible Navier-Stokes approximationconormal derivatives

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Euler equations (35Q31) Boltzmann equations (35Q20) Compressible Navier-Stokes equations (76N06)

Related Items (1)

Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition

Cites Work

• Non-isothermal boundary in the Boltzmann theory and Fourier law
• Uniform regularity and vanishing viscosity limit for the free surface Navier-Stokes equations
• The initial boundary value problem for the Boltzmann equation with soft potential
• Energy method for Boltzmann equation
• Decay and continuity of the Boltzmann equation in bounded domains
• Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids
• Molecular gas dynamics. Theory, techniques, and applications.
• Hydrodynamic limits of the Boltzmann equation
• Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case
• Derivation of slip boundary conditions for the Navier-Stokes system from the Boltzmann equation
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
• The Boltzmann equation and its applications
• Hydrodynamic limit of the stationary Boltzmann equation in a slab
• Asymptotic theory of the Boltzmann system, for a steady flow of a slightly rarefied gas with a finite Mach number: General theory
• The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation.
• The Navier-Stokes limit of the stationary Boltzmann equation for hard potentials.
• Stationary solutions to the Boltzmann equation in the hydrodynamic limit
• Slip boundary conditions for the compressible Navier-Stokes equations
• On Friedrichs inequality, Helmholtz decomposition, vector potentials, and the div-curl lemma
• Remarks on the Euler equation
• The compressible boundary layer and the Boltzmann equation
• Solutions of nonlinear kinetic equations on the level of the Navier- Stokes dynamics
• Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics
• Compressible Navier-Stokes approximation to the Boltzmann equation
• Nonlinear stability of rarefaction waves for the Boltzmann equation
• Uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system in three dimensional bounded domain
• On the initial layer and the existence theorem for the nonlinear Boltzmann equation
• Boltzmann diffusive limit beyond the Navier‐Stokes approximation
• Global Hilbert expansion for the Vlasov-Poisson-Boltzmann system
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains