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Esposito R., Lebowitz J.-L., Marra R.
Hydrodynamic Limit of the Stationary
Boltzmann Equation in a Slab
ABSTRACT. We study the stationary solution of the
Boltzmann equation in a slab with a constant
external force parallel to the boundary and complete
accommodation condition on the walls at a specified
temperature. We 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.