Nonlinear Landau damping and wave operators in sharp Gevrey spaces

We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on \(\T^d\times\R^d\) which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the existence of nonlinear scattering operators associated to the conf...

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Bibliographic Details
Published in:arXiv.org 2024-05
Main Authors: Ionescu, A D, Pausader, B, Wang, X, Widmayer, K
Format: Article
Language:English
Subjects:
Landau damping
Operators
Online Access:Get full text
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Summary:We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on \(\T^d\times\R^d\) which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the existence of nonlinear scattering operators associated to the confined Vlasov-Poisson evolution, as well as suitable injectivity properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these operators. Our results give definitive answers to two well-known open problems in the field, both of them stated in the recent review of Bedrossian [4, Section 6].
ISSN:2331-8422