Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials

François Golse; Cyril Imbert; Luis Silvestre

Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials

Analysis of PDEs 2023-12-19 v1

Authors: François Golse , Cyril Imbert , Luis Silvestre

Abstract

We prove that the set of singular times for weak solutions of the homogeneous Boltzmann equation with very soft potentials constructed as in Villani (1998) has Hausdorff dimension at most $\frac{|\gamma+2s|}{2s}$ with $\gamma \in [-4s,-2s)$ and $s \in (0,1)$ .

Keywords

Boltzmann equation partial regularity very soft potentials weak solutions Hausdorff dimension singular times space-homogeneous

Cite

@article{arxiv.2312.11079,
  title  = {Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials},
  author = {François Golse and Cyril Imbert and Luis Silvestre},
  journal= {arXiv preprint arXiv:2312.11079},
  year   = {2023}
}

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