Non-isothermal boundary in the Boltzmann theory and Fourier law

DOI10.1007/s00220-013-1766-2zbMath1280.82009OpenAlexW2150550863MaRDI QIDQ368557

Yan Guo, Rossana Marra, Raffaele Esposito, Chanwoo Kim

Publication date: 23 September 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-013-1766-2

zbMATH Keywords

nonnegative solutionBoltzmann equationbounded domainunique solutionFourier lawelastic collisionsKnudsen numbernon-isothermal boundary

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Boltzmann equations (35Q20)

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Cites Work

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• Hilbert expansion from the Boltzmann equation to relativistic fluids
• Asymptotic stability of the relativistic Boltzmann equation for the soft potentials
• Ghost effect by curvature in planar Couette flow
• Formation and propagation of discontinuity for Boltzmann equation in non-convex domains
• Decay and continuity of the Boltzmann equation in bounded domains
• Stability for Rayleigh-Benard convective solutions of the Boltzmann equation
• Energy transport in stochastically perturbed lattice dynamics
• Molecular gas dynamics. Theory, techniques, and applications.
• Energy transport in weakly anharmonic chains
• Ordinary differential equations, transport theory and Sobolev spaces
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Phase transition in a Vlasov-Boltzmann binary mixture
• Stochastic formulation for the initial-boundary value problems of the Boltzmann equation
• The Boltzmann equation and its applications
• Hydrodynamic limit of the stationary Boltzmann equation in a slab
• The mathematical theory of dilute gases
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation.
• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
• Kinetic theory and fluid dynamics
• Spectra of perturbed semigroups with applications to transport theory
• The Vlasov-Poisson-Landau system in a periodic box
• Global classical solutions of the Boltzmann equation without angular cut-off
• Acoustic limit for the Boltzmann equation in optimal scaling
• Energy Diffusion and Superdiffusion in Oscillators Lattice Networks
• Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Bounded solutions for the Boltzmann equation
• \(L^1\) solutions to the stationary Boltzmann equation in a slab
• Global Hilbert expansion for the Vlasov-Poisson-Boltzmann system

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