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

Daniel Han-Kwan

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arXiv · 1011.6032

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

Daniel Han-Kwan

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Abstract

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 $\partial_t f + v.\nabla_x f + F.\nabla_v f =0$.

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Daniel Han-Kwan. 2010-11-28. L^1 averaging lemma for transport equations with Lipschitz force fields. https://arxiv.org/abs/1011.6032

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