Dispersive estimates for kinetic transport equation in Besov spaces

Abstract

Although Strichartz estimates have been widely applied for the nonlinear dispersive equations like Schrdinger equation and wave equation in Besov spaces, it is rare in nonlinear kinetic type equations such as Vlasov-Poisson equation. In this paper, we are concerned about the dispersive estimates for the kinetic transport equation in Besov spaces, which could be applied to establish Strichartz estimates in Besov space and further may be exploited to investigate the solutions for Vlasov-Poisson equation and Boltzmann equation in Besov space.