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Global existence and full regularity of the Boltzmann equation without angular cutoff

Radjesvarane Alexandre Yoshinori Morimoto Seiji Ukai C-J Xu Tong Yang

Analysis of PDEs mathscidoc:1912.43934

Communications in Mathematical Physics, 304, (2), 513, 2011.6
We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and <i>C</i> <sup></sup> in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem.
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@inproceedings{radjesvarane2011global,
  title={Global existence and full regularity of the Boltzmann equation without angular cutoff},
  author={Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, C-J Xu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210742548073498},
  booktitle={Communications in Mathematical Physics},
  volume={304},
  number={2},
  pages={513},
  year={2011},
}
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, C-J Xu, and Tong Yang. Global existence and full regularity of the Boltzmann equation without angular cutoff. 2011. Vol. 304. In Communications in Mathematical Physics. pp.513. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210742548073498.
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