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

Laurent Desvillettes (1) , Evelyne Miot (2) , Chiara Saffirio

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 IF - Institut Fourier

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.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Desvillettes, Evelyne Miot, Chiara Saffirio. Polynomial propagation of moments and global existence for a Vlasov–Poisson system with a point charge. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2015, 32 (2), pp.373-400. ⟨10.1016/j.anihpc.2014.01.001⟩. ⟨hal-02006558⟩