Boundary layer solution of the Boltzmann equation for specular boundary condition

Abstract

In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in $L_{x,v}^2\cap L_{x,v}^{\infty }$ in half-space. The uniqueness, continuity and exponential decay of the solution are obtained, and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.

28 pages, Comments are welcome. arXiv admin note: text overlap with arXiv:1807.05700