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

François Golse (1) , Cyril Imbert (2) , Luis Silvestre (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 University of Chicago

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 $s \in (0,1)$.

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Cyril Imbert, Luis Silvestre. Partial regularity in time for the space-homogeneous Boltzmann equation with very soft potentials. 2023. ⟨hal-04349073⟩