SMOOTHING EFFECT FOR THE NONLINEAR VLASOV-POISSON-FOKKER-PLANCK SYSTEM

We study a smoothing effect of a non-linear degenerate parabolic probl em, the Vlasov-Poisson-Fokker-Planck system, in three dimensions. We p rove that a solution gives rise actually to very smooth macroscopic de nsity and force field for positive time. This is obtained by analyzing the effect of the Fokker-Planck kernel on the force term in the Vlaso v equation and using classical convolution inequalities. (C) 1995 Acad emic Press, Inc.