English

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

Analysis of PDEs 2021-05-11 v4

Abstract

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.

Keywords

Cite

@article{arxiv.1909.12762,
  title  = {L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system},
  author = {Lanoir Addala and Jean Dolbeault and Xingyu Li and Mohamed Lazhar Tayeb},
  journal= {arXiv preprint arXiv:1909.12762},
  year   = {2021}
}