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

2020/09/16 by Sakamoto, Shota, Suzuki, Masahiro, Zhang, Katherine Zhiyuan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.07798

Abstract

We consider the nonlinear boundary layers of the Boltzmann equation in a three-dimensional half-space by perturbing around a Maxwellian, under the assumption that the Mach number of the Maxwellian satisfies \cal M_∞ < -1. In preceding works, nonlinear boundary layers of the Boltzmann equation in a half-line are considered, with stationary solutions obtained and nonlinear stability confirmed. In this paper, we establish the unique existence of stationary solutions for the three-dimensional half-space model, and show that the stationary solution is asymptotic stable.

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