Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space

Tong Yang Hongjun Yu

Analysis of PDEs mathscidoc:1912.43949

Journal of Differential Equations, 248, (6), 1518-1560, 2010.3
We study the hypocoercivity property for some kinetic equations in the whole space and obtain the optimal convergence rates of solutions to the equilibrium state in some function spaces. The analysis relies on the basic energy method and the compensating function introduced by Kawashima to the classical Boltzmann equation and developed by Glassey and Strauss in the relativistic setting. It is also motivated by the recent work (Duan et al., 2008 [8]) on the Boltzmann equation by combining the spectrum analysis and energy method. The advantage of the method introduced in this paper is that it can be applied to some complicated system whose detailed spectrum is not known. In fact, only some estimates through the Fourier transform on the conservative transport operator and the dissipation of the linearized operator on the subspace orthogonal to the collision invariants are needed.
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@inproceedings{tong2010hypocoercivity,
  title={Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space},
  author={Tong Yang, and Hongjun Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210841789524513},
  booktitle={Journal of Differential Equations},
  volume={248},
  number={6},
  pages={1518-1560},
  year={2010},
}
Tong Yang, and Hongjun Yu. Hypocoercivity of the relativistic Boltzmann and Landau equations in the whole space. 2010. Vol. 248. In Journal of Differential Equations. pp.1518-1560. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210841789524513.
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