## 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 language | English (US) |
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Pages (from-to) | 389-412 |

Number of pages | 24 |

Journal | Journal of Statistical Physics |

Volume | 78 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 1995 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

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