Nonlinear stability of rarefaction waves for the Boltzmann equation

Tai-Ping Liu Tong Yang Shih-Hsien Yu Hui-Jiang Zhao

Analysis of PDEs mathscidoc:1912.43941

Archive for rational mechanics and analysis, 181, (2), 333-371, 2006.7
It is well known that the Boltzmann equation is related to the Euler and Navier-Stokes equations in the field of gas dynamics. The relation is either for small Knudsen number, or, for dissipative waves in the time-asymptotic sense. In this paper, we show that rarefaction waves for the Boltzmann equation are time-asymptotic stable and tend to the rarefaction waves for the Euler and Navier-Stokes equations. Our main tool is the combination of techniques for viscous conservation laws and the energy method based on micro-macro decomposition of the Boltzmann equation. The expansion nature of the rarefaction waves and the suitable microscopic version of the <i>H</i>-theorem are essential elements of our analysis.
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@inproceedings{tai-ping2006nonlinear,
  title={Nonlinear stability of rarefaction waves for the Boltzmann equation},
  author={Tai-Ping Liu, Tong Yang, Shih-Hsien Yu, and Hui-Jiang Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210809001301505},
  booktitle={Archive for rational mechanics and analysis},
  volume={181},
  number={2},
  pages={333-371},
  year={2006},
}
Tai-Ping Liu, Tong Yang, Shih-Hsien Yu, and Hui-Jiang Zhao. Nonlinear stability of rarefaction waves for the Boltzmann equation. 2006. Vol. 181. In Archive for rational mechanics and analysis. pp.333-371. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210809001301505.
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