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

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 Bol...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 314; pp. 446 - 472
Main Authors Sakamoto, Shota, Suzuki, Masahiro, Zhang, Katherine Zhiyuan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.03.2022
Subjects
Asymptotic stability
Boltzmann equation
Boundary layers
Stationary solution
Time-periodic solution
Asymptotic stability
Boltzmann equation
76P05
82C40
Stationary solution
35Q20
35B40
Boundary layers
Time-periodic solution
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.01.023