Elsevier

Journal of Functional Analysis

Volume 271, Issue 5, 1 September 2016, Pages 1301-1340
Journal of Functional Analysis

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

https://doi.org/10.1016/j.jfa.2016.04.030Get rights and content
Under an Elsevier user license
open archive

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.

MSC

35Q83
35Q84
35B40

Keywords

Vlasov–Poisson–Fokker–Planck equation
Non-self-adjoint operator
Global solutions
Return to equilibrium

Cited by (0)

F.H. is supported by the grant “NOSEVOLANR-2011-BS01019-01. L.T. is supported by the grant “ANAÉANR-13-BS01-0010-03. The authors warmly thank Jean Dolbeault for enriching discussions and are grateful to Laurent Di Menza who was at the origin of this collaboration.