Global existence of weak solutions to the nonlinear Vlasov-Fokker-Planck equation

Abstract

In this paper, we study the nonlinear Vlasov-Fokker-Planck equation with fixed collision frequency. We establish the global-in-time existence of weak solutions to the equation with large initial data. Moreover, we show that our solution satisfies the conservation laws of mass, momentum, and energy, and Boltzmann's $H$-theorem.