Polynomial propagation of moments and global existence for a Vlasov–Poisson system with a point charge
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 2, pp. 373-400.

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 [8] for the Vlasov–Poisson equation. Our techniques also provide polynomially growing in time estimates for moments of the bounded density.

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     author = {Desvillettes, Laurent and Miot, Evelyne and Saffirio, Chiara},
     title = {Polynomial propagation of moments and global existence for a {Vlasov{\textendash}Poisson} system with a point charge},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {373--400},
     publisher = {Elsevier},
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     year = {2015},
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Desvillettes, Laurent; Miot, Evelyne; Saffirio, Chiara. Polynomial propagation of moments and global existence for a Vlasov–Poisson system with a point charge. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 2, pp. 373-400. doi : 10.1016/j.anihpc.2014.01.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.01.001/

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