Combined quasineutral and inviscid limit of the Vlasov-Poisson-Fokker-Planck system

Ling Hsiao; Fucai Li; Shu Wang

doi:10.3934/cpaa.2008.7.579

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2008, Volume 7, Issue 3: 579-589. Doi: 10.3934/cpaa.2008.7.579

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Combined quasineutral and inviscid limit of the Vlasov-Poisson-Fokker-Planck system

1.
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080
2.
Department of Mathematics, Nanjing University, Nanjing 210093
3.
College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022

Received: March 31, 2007

Revised: September 30, 2007

Published: April 2008

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Abstract

The combined quasineutral and inviscid limit for the Vlasov-Poisson-Fokker-Planck (VPFP) system is rigorously derived in this paper. It is shown that the solution of VPFP system converges to the solution of incompressible Euler equations with damping. The proof of convergence result is based on compactness arguments and the so-called relative-entropy method.

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Mathematics Subject Classification: 35F20, 35B40, 82D10.

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