Smoothness of classical solutions to the Vlasov-Poisson-Landau system

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September 2008, 1(3): 369-386. doi: 10.3934/krm.2008.1.369

Smoothness of classical solutions to the Vlasov-Poisson-Landau system

1.	Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received March 2008 Revised June 2008 Published August 2008

Abstract
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In this paper we prove that any classical solutions to the Vlasov-Poisson-Landau system (such as the one obtained by Yu in the case being near Maxwellians) become immediately smooth with respect to all variables. This implies that the Vlasov-Poisson-Landau system is a nonlinear and nonlocal analog of an hypoelliptic equation.

Keywords: Smoothness, averaging lemmas., Vlasov-Poisson-Landau system.

Mathematics Subject Classification: Primary: 35B65, 35Q60; Secondary: 82D1.

Citation: Yemin Chen. Smoothness of classical solutions to the Vlasov-Poisson-Landau system. Kinetic & Related Models, 2008, 1 (3) : 369-386. doi: 10.3934/krm.2008.1.369

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