93-77 Esposito R., Lebowitz J.-L., Marra R.

Hydrodynamic Limit of the Stationary Boltzmann Equation in a Slab (88K, Ams-TeX) Apr 1, 93

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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.

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