Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang

doi:10.1215/21562261-1625154

Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

Analysis of PDEs 2015-01-14 v1

Authors: Radjesvarane Alexandre , Yoshinori Morimoto , Seiji Ukai , Chao-Jiang Xu , Tong Yang

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Abstract

In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^\infty$ regularity in the velocity variable for the positive time.

Keywords

Boltzmann equation spatially homogeneous without angular cutoff weak solutions smoothing effect C^\infty regularity Cauchy problem

Cite

@article{arxiv.1104.5648,
  title  = {Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff},
  author = {Radjesvarane Alexandre and Yoshinori Morimoto and Seiji Ukai and Chao-Jiang Xu and Tong Yang},
  journal= {arXiv preprint arXiv:1104.5648},
  year   = {2015}
}

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