Nonlinear stability of boundary layer solution to the Boltzmann equation with diffusive effect at the boundary

Abstract

In this paper, the stability of boundary layer solutions to the Boltzmann equation with diffusive effect at the boundary for hard sphere model is considered. When the Mach number of the far field is less than −1, the exponential decay in time is proven for linearized operator first. At last, based on this property, nonlinear stability of the boundary layers is obtained by bootstrap argument.