Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

Teng Wang; Yi Wang

doi:10.3934/krm.2019025

Article Contents

2019, Volume 12, Issue 3: 637-679. Doi: 10.3934/krm.2019025

This issue Previous Article Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations Next Article

Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

Teng Wang^1, and
Yi Wang^2,3, ,

1.
College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
2.
CEMS, HCMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^* Corresponding author: Yi Wang
^* Corresponding author: Yi Wang

Received: September 2018

Revised: November 2018

Published: June 2019

The first author is supported by NSFC Grant No. 11601031. The second author is supported by NSFC grants No. 11671385 and 11688101 and CAS Interdisciplinary Innovation Team.

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Abstract

We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24,22] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of planar rarefaction wave for 3D Boltzmann equation, while the corresponding results for the shock and contact discontinuities are still completely open.

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Mathematics Subject Classification: Primary: 35Q20, 76P05, 74J40; Secondary: 35L65.

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