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

Shota Sakamoto; Masahiro Suzuki; Katherine Zhiyuan Zhang

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arXiv · 2009.07798

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

Shota Sakamoto·Masahiro Suzuki·Katherine Zhiyuan Zhang

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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 ${\cal M}_{\infty} < -1$. 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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Shota Sakamoto, Masahiro Suzuki, Katherine Zhiyuan Zhang. 2020-09-16. Boundary layers of the Boltzmann equation in a three-dimensional half-space. https://arxiv.org/abs/2009.07798

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