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

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.

arXiv comment27 pages; new version: few typos have been corrected, the introduction has been modified