10.1007/s10955-021-02784-4
https://zenodo.org/records/5747811
oai:zenodo.org:5747811
Addala, Lanoir
Lanoir
Addala
Dolbeault, Jean
Jean
Dolbeault
0000-0003-4234-2298
Li, Xingyu
Xingyu
Li
Tayeb, M. Lazhar
M. Lazhar
Tayeb
$\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System
Zenodo
2021
2021-06-21
Free for private use; right holder retains other rights, including distribution
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.