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arXiv · 1505.01698

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

Frédéric Hérau·Laurent Thomann
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Abstract

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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Frédéric Hérau, Laurent Thomann. 2015-05-07. On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential. https://arxiv.org/abs/1505.01698

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