The Boltzmann equation without angular cutoff. Global existence and full regularity of the Boltzmann equation without angular cutoff. Part I: Maxwellian case and small singularity.

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

Analysis of PDEs mathscidoc:1912.431007

The global existence and uniqueness of classical solutions to the Boltzmann equation without angular cut-off is proved under the condition that the initial data is in some Sobolev space. In addition, the solutions thus obtained are shown to be positive and C in all variables. One of the key observations is the introduction of a new important norm related to the singularity in the cross section of the collision operator. This norm captures the essential property of the singularity and yields precisely the dissipation description of the linearized collision operator through the celebrated H-theorem.
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@inproceedings{radjesvaranethe,
  title={The Boltzmann equation without angular cutoff. Global existence and full regularity of the Boltzmann equation without angular cutoff. Part I: Maxwellian case and small singularity.},
  author={Radjesvarane Alexandre, Y Morimoto, Seiji Ukai, Chao-Jiang Xu, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211204560950571},
}
Radjesvarane Alexandre, Y Morimoto, Seiji Ukai, Chao-Jiang Xu, and Tong Yang. The Boltzmann equation without angular cutoff. Global existence and full regularity of the Boltzmann equation without angular cutoff. Part I: Maxwellian case and small singularity.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211204560950571.
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