L^1 averaging lemma for transport equations with Lipschitz force fields

Daniel Han-Kwan (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

The purpose of this note is to extend the $L^1$ averaging lemma of Golse and Saint-Raymond \cite{GolSR} to the case of a kinetic transport equation with a force field $F(x)\in W^{1,\infty}$. To this end, we will prove a local in time mixing property for the transport equation $\partial_t f + v.\nabla_x f + F.\nabla_v f =0$.

Domaines: Equations aux dérivées partielles [math.AP]

Daniel Han-Kwan. L^1 averaging lemma for transport equations with Lipschitz force fields. 2010. ⟨hal-00540200⟩