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Energy method for Boltzmann equation

Tai-Ping Liu Tong Yang Shih-Hsien Yu

Analysis of PDEs mathscidoc:1912.43926

Physica D: Nonlinear Phenomena, 188, 178-192, 2004.2
A basic, simple energy method for the Boltzmann equation is presented here. It is based on a new macromicro decomposition of the Boltzmann equation as well as the H-theorem. This allows us to make use of the ideas from hyperbolic conservation laws and viscous conservation laws to yield the direct energy method. As an illustration, we apply the method for the study of the time-asymptotic, nonlinear stability of the global Maxwellian states. Previous energy method, starting with Grad and finishing with Ukai, involves the spectral analysis and regularity of collision operator through sophisticated weighted norms.
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@inproceedings{tai-ping2004energy,
  title={Energy method for Boltzmann equation},
  author={Tai-Ping Liu, Tong Yang, and Shih-Hsien Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210714516141490},
  booktitle={Physica D: Nonlinear Phenomena},
  volume={188},
  pages={178-192},
  year={2004},
}
Tai-Ping Liu, Tong Yang, and Shih-Hsien Yu. Energy method for Boltzmann equation. 2004. Vol. 188. In Physica D: Nonlinear Phenomena. pp.178-192. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210714516141490.
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