Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces

Abstract

In this paper, we are concerned with the local well-posedness of the Vlasov-Poisson-Fokker-Planck equation near vacuum in the fractional Sobolev-Lebesgue space for the large initial data. To achieve this goal, we mainly adopt the energy method. In order to obtain the energy estimate, we establish an L²-L^q estimate related to the electronic term, and take advantage of the commutator estimates as well.