EXISTENCE OF BOUNDARY LAYER SOLUTIONS TO THE BOLTZMANN EQUATION

Abstract

In this paper, we consider the existence of boundary layer solutions to the Boltzmann equation for a hard potential with angular cut-off. The boundary condition is imposed for incoming particles of Dirichlet type and the solution tends to a global Maxwellian in the far field. Similar to the problem on the hard sphere model studied in [17], the existence of a solution is shown to depend on the Mach number of the far field Maxwellian, and there is an implicit solvability conditions yielding the co-dimensions of the boundary data. For hard potential models, the shape of the boundary layers is richer. This compels the introduction of a new norm which is a function of both position and velocity.