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Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum

Yoshinori Morimoto Tong Yang

Analysis of PDEs mathscidoc:1912.43971

Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 32, (2), 429-442, 2015.3
We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.
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@inproceedings{yoshinori2015smoothing,
  title={Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum},
  author={Yoshinori Morimoto, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211003036704535},
  booktitle={Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
  volume={32},
  number={2},
  pages={429-442},
  year={2015},
}
Yoshinori Morimoto, and Tong Yang. Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum. 2015. Vol. 32. In Annales de l'Institut Henri Poincare (C) Non Linear Analysis. pp.429-442. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211003036704535.
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