The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation.

DOI10.1007/BF02183355zbMath1078.82525MaRDI QIDQ1593168

Rossana Marra, Raffaele Esposito, Joel L. Lebowitz

Publication date: 16 January 2001

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

zbMATH Keywords

kinetic theorystationary Navier-Stokes equationsHydrodynamic limit

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (15)

Stationary solutions to the Boltzmann equation in the hydrodynamic limit ⋮ Non-isothermal boundary in the Boltzmann theory and Fourier law ⋮ Asymptotic behavior on the Milne problem with a force term ⋮ Stationary non equilibrium states in kinetic theory ⋮ On the derivation of hydrodynamics from the Boltzmann equation ⋮ Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains ⋮ The initial boundary value problem for the Boltzmann equation with soft potential ⋮ The milne problem with a force term ⋮ The stationary nonlinear Boltzmann equation in a Couette setting with multiple, isolated \(L^q\)-solutions and hydrodynamic limits ⋮ A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation ⋮ Stability for Rayleigh-Benard convective solutions of the Boltzmann equation ⋮ Existence of a nonequilibrium steady state for the nonlinear BGK equation on an interval ⋮ Effects of soft interaction and non-isothermal boundary upon long-time dynamics of rarefied gas ⋮ The Navier-Stokes limit of the stationary Boltzmann equation for hard potentials. ⋮ Heat transfer problem for the Boltzmann equation in a channel with diffusive boundary condition

Cites Work

• On a boundary layer problem for the nonlinear Boltzmann equation
• The Boltzmann equation and its applications
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• Hydrodynamic limit of the stationary Boltzmann equation in a slab
• Incompressible navier-stokes and euler limits of the boltzmann equation
• On the StrongL¹Trend to Equilibrium for the Boltzmann Equation
• Asymptotic Theory of the Boltzmann Equation
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