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

R. Esposito, J. L. Lebowitz, R. Marra

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30 Scopus citations

Abstract

We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.

Original languageEnglish (US)
Pages (from-to)389-412
Number of pages24
JournalJournal of Statistical Physics
Volume78
Issue number1-2
DOIs
StatePublished - Jan 1995

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Hydrodynamic limit
  • kinetic theory
  • stationary Navier-Stokes equations

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