Boundary layers of the Boltzmann equation in three-dimensional half-space

Abstract

We consider the nonlinear boundary layers of the Boltzmann equation on a three-dimensional half-space by perturbing around a Maxwellian under the assumption that the Mach number of the Maxwellian satisfies M∞<−1. In earlier works by S. Ukai, T. Yang, S.-H. Yu, nonlinear boundary layers of the Boltzmann equation in a half-line are considered, in a half-line are considered, the stationary solutions were obtained and nonlinear stability was confirmed. We establish the existence and uniqueness of stationary and time-periodic solutions for the three-dimensional half-space model and show that these solutions are asymptotically stable.