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Landau Damping for the Linearized Vlasov Poisson Equation in a Weakly Collisional Regime

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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 \({\varepsilon }\) 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 \({\varepsilon }\) as it goes to 0.

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Acknowledgements

The author would like to thank Daniel Han-Kwan for enlightened discussions, his help and his suggestions. The author has been supported by the Fondation Mathématique Jacques Hadamard.

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  1. Centre de Mathématiques Laurent Schwartz, École polytechnique, CNRS, Université Paris-Saclay, 91128, Palaiseau Cedex, France

    Isabelle Tristani

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  1. Isabelle Tristani
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Correspondence to Isabelle Tristani.

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Tristani, I. Landau Damping for the Linearized Vlasov Poisson Equation in a Weakly Collisional Regime. J Stat Phys 169, 107–125 (2017). https://doi.org/10.1007/s10955-017-1848-1

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  • DOI: https://doi.org/10.1007/s10955-017-1848-1

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