Journal of Statistical Physics

, Volume 78, Issue 1–2, pp 389–412 | Cite as

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

  • R. Esposito
  • J. L. Lebowitz
  • R. Marra
Articles

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.

Key Words

Hydrodynamic limit stationary Navier-Stokes equations kinetic theory 

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • R. Esposito
    • 1
  • J. L. Lebowitz
    • 2
  • R. Marra
    • 3
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomeItaly
  2. 2.Mathematics and Physics DepartmentsRutgers UniversityNew Brunswick
  3. 3.Dipartimento di FisicaUniversità di Roma Tor VergataRomeItaly

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