Global Existence to the Vlasov–Poisson System and Propagation of Moments Without Assumption of Finite Kinetic Energy

Abstract

We consider classical as well as weak solutions to the three dimensional Vlasov–Poisson system. Without assuming finiteness of kinetic energy, we prove global existence of classical solutions by assuming the initial datum is smooth enough and has a compact velocity-spatial support, which will be specified in Theorem 1.1. We also establish some propagation results for low moments of weak solutions.