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, p. 373-400
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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.

@article{AIHPC_2015__32_2_373_0,
     author = {Desvillettes, Laurent and Miot, Evelyne and Saffirio, Chiara},
     title = {Polynomial propagation of moments and global existence for a Vlasov--Poisson system with a point charge},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {2},
     year = {2015},
     pages = {373-400},
     doi = {10.1016/j.anihpc.2014.01.001},
     zbl = {1323.35178},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_2_373_0}
}
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://www.numdam.org/item/AIHPC_2015__32_2_373_0/

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