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

Addala, Lanoir; Dolbeault, Jean; Li, Xingyu; Lazhar Tayeb, Mohamed (2021), L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system, Journal of Statistical Physics, 184. 10.1007/s10955-021-02784-4

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Type
Article accepté pour publication ou publié
Date
2021
Nom de la revue
Journal of Statistical Physics
Volume
184
Éditeur
Springer
Identifiant publication
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Auteur(s)
Addala, Lanoir
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Li, Xingyu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lazhar Tayeb, Mohamed
Résumé (EN)
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.
Mots-clés
diffusion limit; drift-diffusion equations; hypocoercivity; Vlasov–Poisson-Fokker–Planck system; convergence to equilibrium; confinement; electrostatic forces; Poisson coupling; Fokker-Planck operator; Vlasov equation; large-time behavior; rate of convergence