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Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff

Zhaohui Huo Yoshinori Morimoto Seiji Ukai Tong Yang

Analysis of PDEs mathscidoc:1912.43936

Kinetic & Related Models, 1, (3), 453, 2008.8
The spatially homogeneous Boltzmann equation without angular cutoff is discussed on the regularity of solutions for the modified hard potential and Debye-Yukawa potential. When the angular singularity of the cross section is moderate, any weak solution having the finite mass, energy and entropy lies in the Sobolev space of infinite order for any positive time, while for the general potentials, it lies in the Schwartz space if it has moments of arbitrary order. The main ingredients of the proof are the suitable choice of the mollifiers composed of pseudo-differential operators and the sharp estimates of the commutators of the Boltzmann collision operator and pseudo-differential operators. The method developed here also provides some new estimates on the collision operator.
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@inproceedings{zhaohui2008regularity,
  title={Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff},
  author={Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210749431888500},
  booktitle={Kinetic & Related Models},
  volume={1},
  number={3},
  pages={453},
  year={2008},
}
Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, and Tong Yang. Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff. 2008. Vol. 1. In Kinetic & Related Models. pp.453. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210749431888500.
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