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arXiv · 1909.12762

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

Lanoir Addala·Jean Dolbeault·Xingyu Li·Mohamed Lazhar Tayeb
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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.

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Lanoir Addala, Jean Dolbeault, Xingyu Li, Mohamed Lazhar Tayeb. 2019-09-27. L2-Hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system. https://arxiv.org/abs/1909.12762

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