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

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