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

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.
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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