Polynomial propagation of moments and global existence for a Vlasov-Poisson system with a point charge

TL;DR

This paper extends the theory of Vlasov-Poisson equations to include initial data with a Dirac mass and bounded density, providing polynomial growth estimates for moments over time.

Contribution

It introduces a novel extension of Lions and Perthame's theory to cases with point charges and bounded densities, with new polynomial growth estimates.

Findings

Extended Vlasov-Poisson theory to Dirac mass plus bounded density

Derived polynomial growth estimates for moments

Applicable to systems with point charges

Abstract

In this paper, we extend to the case of initial data constituted of a Dirac mass plus a bounded density (with finite moments) the theory of Lions and Perthame [6] for the Vlasov-Poisson equation. Our techniques also provide polynomially growing in time estimates for moments of the bounded density.