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Regularity of solutions for the Boltzmann equation without angular cutoff

Radjesvarane Alexandre Yoshinore Morimoto Seiji Ukai Chao-Jiang Xu Tong Yang

Analysis of PDEs mathscidoc:1912.43985

Comptes Rendus Mathematique, 347, 747-752, 2009.7
We prove that classical solution of the spatially inhomogeneous and angular non-cutoff Boltzmann equation is C with respect to all variables, locally in the space and time variables. The proof relies on a generalized uncertainty principle, some improved upper bound and coercivity estimates on the nonlinear collision operator, and some subtle analysis on the commutators between the collision operators and some appropriately chosen pseudo-differential operators. To cite this article: R. Alexandre et al., CR Acad. Sci. Paris, Ser. I 347 (2009).
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@inproceedings{radjesvarane2009regularity,
  title={Regularity of solutions for the Boltzmann equation without angular cutoff},
  author={Radjesvarane Alexandre, Yoshinore Morimoto, Seiji Ukai, Chao-Jiang Xu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211051945125549},
  booktitle={Comptes Rendus Mathematique},
  volume={347},
  pages={747-752},
  year={2009},
}
Radjesvarane Alexandre, Yoshinore Morimoto, Seiji Ukai, Chao-Jiang Xu, and Tong Yang. Regularity of solutions for the Boltzmann equation without angular cutoff. 2009. Vol. 347. In Comptes Rendus Mathematique. pp.747-752. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211051945125549.
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