Publication 15-CNA-019

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

Lei Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
lwu2@andrew.cmu.edu

Abstract: We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. The classical theory claims that the solution can be approximated by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer derived from Milne problem. In this paper, we construct counterexamples to disprove such formulation in $L^{\infty}$ both for its proof and result. Also, we show the hydrodynamic limit with a different boundary layer expansion with geometric correction.

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