Propagation of moments and uniqueness of weak solution to Vlasov-Poisson-Fokker-Planck system

Ze Li, Lifeng Zhao

Published 2015-03-15Version 1

In this paper, we prove the uniqueness of weak solution to Vlasov-Poisson-Fokker-Planck system in $C([0,T]; L^p)$, by assuming the solution has local bounded density which trends to infinite with a "reasonable" rate as $t$ trends zero. And particularly as a corollary, we get uniqueness of weak solution with initial data $f_0$ satisfying $f_0|v|^2\in L^1$, which solves the uniqueness of solutions with finite energy. In addition, we prove that the moments in velocity propagate for any order higher than 2.