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Article Dans Une Revue Journal of Statistical Physics Année : 2021

L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system

Lanoir Addala
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M Lazhar Tayeb
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Résumé

This paper is devoted to the linearized Vlasov-Poisson-Fokker-Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov-Poisson-Fokker-Planck system without any small mass assumption.
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Dates et versions

hal-02299535 , version 1 (27-09-2019)
hal-02299535 , version 2 (07-10-2019)
hal-02299535 , version 3 (31-12-2020)
hal-02299535 , version 4 (10-05-2021)

Identifiants

Citer

Lanoir Addala, Jean Dolbeault, Xingyu Li, M Lazhar Tayeb. L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system. Journal of Statistical Physics, 2021, 184 (1), pp.4. ⟨10.1007/s10955-021-02784-4⟩. ⟨hal-02299535v4⟩
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