# American Institute of Mathematical Sciences

March  2008, 1(1): 139-170. doi: 10.3934/krm.2008.1.139

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

 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, France

Received  November 2007 Revised  November 2007 Published  February 2008

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.
Citation: Mihai Bostan, Thierry Goudon. Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case. Kinetic & Related Models, 2008, 1 (1) : 139-170. doi: 10.3934/krm.2008.1.139
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