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

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

2010-11-28

arxiv.org/abs/1011.6032v1

Mathematics

Analysis of PDEs

15 pages, to be published in Kinetic and Related Models

Scientific paper

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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