Short time diffusion properties of inhomogeneous kinetic equations with fractional collision kernel

Frédéric Hérau (1) , Daniela Tonon (2) , Isabelle Tristani (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 DMA - Département de Mathématiques et Applications - ENS Paris

We prove regularization properties in short time for inhomogeneous kinetic equations whose collision kernel behaves like a fractional power of the Laplacian in velocity. We treat a fractional Kolmogorov equation and the linearized Boltzmann equation without cutoff (for hard potentials).

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Hérau, Daniela Tonon, Isabelle Tristani. Short time diffusion properties of inhomogeneous kinetic equations with fractional collision kernel. 2018. ⟨hal-01596009v2⟩