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$\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov–Poisson–Fokker–Planck System

Addala, Lanoir; Dolbeault, Jean; Li, Xingyu; Tayeb, M. Lazhar


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    "description": "This paper is devoted to the linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck 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\u2013Poisson\u2013Fokker\u2013Planck system without any small mass assumption.", 
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    "title": "$\\text {L}^2$-Hypocoercivity and Large Time Asymptotics of the Linearized Vlasov\u2013Poisson\u2013Fokker\u2013Planck System", 
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