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

Daniel Han-Kwan

doi:10.3934/krm.2010.3.669

Article Contents

2010, Volume 3, Issue 4: 669-683. Doi: 10.3934/krm.2010.3.669

This issue Previous Article Analytic regularity for solutions of the spatially homogeneous Landau-Fermi-Dirac equation for hard potentials Next Article Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity

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

Daniel Han-Kwan^1,

1.
École Normale Suprieure, Dpartement de Mathmatiques et Applications, 75230 Paris Cedex 05

Received: March 31, 2010

Revised: August 31, 2010

Published: November 2010

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Abstract

The purpose of this note is to extend the $L^1$ averaging lemma of Golse and Saint-Raymond [10] 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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Mathematics Subject Classification: Primary: 35Q83; Secondary: 82C70.

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