Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case

Mihai Bostan; Thierry Goudon

doi:10.3934/krm.2008.1.139

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2008, Volume 1, Issue 1: 139-170. Doi: 10.3934/krm.2008.1.139

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Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case

Mihai Bostan^1, and
Thierry Goudon^2,

1.
Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, Besançon, 25030 Cedex
2.
INRIA Project Team SIMPAF & Laboratoire Paul Painlevé, UMR CNRS 8524, INRIA Research Centre Futurs, Park Plazza 40, avenue Halley, 59650 Villeneuve d'Ascq

Received: October 31, 2007

Revised: October 31, 2007

Published: February 2008

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Abstract

We study the asymptotic regime for the relativistic Vlasov-Maxwell-Fokker-Planck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in the one and one half dimensional case and the proof combines dissipation mechanisms and finite speed of propagation properties.

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Mathematics Subject Classification: Primary: 35Q99, 35B40.

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