Partial regularity in time for the space homogeneous Landau equation with Coulomb potential

François Golse (1) , Maria Pia Gualdani (2) , Cyril Imbert (3, 4) , Alexis Vasseur (5)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 GW - Department of Mathematics [George Washington University]
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 CNRS - Centre National de la Recherche Scientifique
5 University of Texas at Austin [Austin]

We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal. 143 (1998), 273-307] has Hausdorff dimension at most 1/2.

Domaines: Equations aux dérivées partielles [math.AP]

François Golse, Maria Pia Gualdani, Cyril Imbert, Alexis Vasseur. Partial regularity in time for the space homogeneous Landau equation with Coulomb potential. Annales Scientifiques de l'École Normale Supérieure, 2022, 55 (4ème série) (6), pp.1575-1611. ⟨10.24033/asens.2524⟩. ⟨hal-02145096⟩