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Article Dans Une Revue Journal of Functional Analysis Année : 2016

On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential

Laurent Thomann

Résumé

We prove a global existence result with initial data of low regularity, and prove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with small non linear term but with a possibly large exterior confining potential in dimension $d=2$ and $d=3$. The proof relies on a fixed point argument using sharp estimates (at short and long time scales) of the semi-group associated to the Fokker-Planck operator, which were obtained by the first author.
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Dates et versions

hal-01147848 , version 1 (02-05-2015)
hal-01147848 , version 2 (05-05-2016)

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Citer

Frédéric Hérau, Laurent Thomann. On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential. Journal of Functional Analysis, 2016, 271 (5), pp.1301--1340. ⟨10.1016/j.jfa.2016.04.030⟩. ⟨hal-01147848v2⟩
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