Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime

Abstract

In this paper, we consider the linearized Vlasov-Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter $\eps$ in front of the collision operator which will tend to $0$. Moreover, we study two cases of collision operators, linear Boltzmann and Fokker-Planck. We prove a result of Landau damping for those equations in Sobolev spaces uniformly with respect to the collision parameter $\eps$ as it goes to $0$.

References in corpus (3)

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• Landau damping in Sobolev spaces for the Vlasov-HMF model
• The Vlasov-Poisson-Boltzmann system for the whole range of cutoff soft potentials

Cited by in corpus (5)

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• Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
• The linearized Vlasov and Vlasov-Fokker-Planck equations in a uniform magnetic field
• Long time estimates for the Vlasov-Maxwell system in the non-relativistic limit
• Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation