Hydrodynamic Limit of the Stationary Boltzmann Equation in a Slab

摘要

The authors study the stationary solution of the Boltzmann equation in a slabwith a constant external force parallel to the boundary and complete accommodation condition on the walls at a specified temperature. The authors prove that when the force is sufficiently small, there exists 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 boundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.