Time evolution of a plasma-charge system with infinite mass and velocities

Abstract

We are concerned with the three dimensional Vlasov-Poisson plasma interacting with a like point charge in the case of infinite mass and velocities. We prove the global existence and uniqueness of the classical solution to the system by assuming that the initial density slightly decays in space variables and strongly decays in velocities. This result generalizes the previous one for the initial data compactly supported in velocities, moreover, our method fills up some gaps of reference [39].