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The Boltzmann equation with soft potentials near a local Maxwellian

Zhouping Xin Tong Yang Hongjun Yu

Analysis of PDEs mathscidoc:1912.43997

Archive for Rational Mechanics and Analysis, 206, (1), 239, 2012.10
In this paper, we consider the Boltzmann equation with soft potentials and prove the stability of a class of non-trivial profiles defined as some given local Maxwellians. The method consists of the analytic techniques for viscous conservation laws, properties of Burnett functions and energy method through the micro-macro decomposition of the Boltzmann equation. In particular, one of the key observations is a detailed analysis of the Burnett functions so that the energy estimates can be obtained in a clear way. As an application of the main results in this paper, we prove the large time nonlinear asymptotic stability of rarefaction waves to the Boltzmann equation with soft potentials.
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@inproceedings{zhouping2012the,
  title={The Boltzmann equation with soft potentials near a local Maxwellian},
  author={Zhouping Xin, Tong Yang, and Hongjun Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211129121882561},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={206},
  number={1},
  pages={239},
  year={2012},
}
Zhouping Xin, Tong Yang, and Hongjun Yu. The Boltzmann equation with soft potentials near a local Maxwellian. 2012. Vol. 206. In Archive for Rational Mechanics and Analysis. pp.239. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211129121882561.
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