On the 3-D Vlasov–Poisson system with point charges: Global solutions with unbounded supports and propagation of velocity-spatial moments

Abstract

A new energy functional, which is shown to decay to zero as time tends to infinite, is introduced for the three-dimensional Vlasov–Poisson plasma in the presence of heavy point charges with repulsive interaction. Moreover, a new kind of pointwise energy of a plasma particle relative to each point charge is also constructed and the variation of its root is shown to be controlled by the electrostatic fields. Based on those results, we prove global existence and uniqueness of a classical solution possibly having infinite kinetic energy, but with compact “velocity-spatial support” specified in Theorem 1.1. Furthermore, for the single point charge-Vlasov–Poisson plasma, global existence and polynomial propagation of “velocity-spatial moments” of weak solutions are also established.