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arXiv · 2405.04473

Nonlinear Landau damping and wave operators in sharp Gevrey spaces

A. D. Ionescu·B. Pausader·X. Wang·K. Widmayer
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Abstract

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].

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A. D. Ionescu, B. Pausader, X. Wang, K. Widmayer. 2024-05-07. Nonlinear Landau damping and wave operators in sharp Gevrey spaces. https://arxiv.org/abs/2405.04473

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