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Mathematical Research Letters
Volume 28 (2021)
Number 6
Landau damping for analytic and Gevrey data
Pages: 1679 – 1702
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n6.a3
Authors
Abstract
In this paper, we give an elementary proof of the nonlinear Landau damping for the Vlasov–Poisson system near Penrose stable equilibria on the torus $\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and Villani in [9] for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot [2] for Gevrey‑$\gamma$ data, $\gamma \in (\frac{1}{3},1]$. Our proof relies on simple pointwise resolvent estimates and a standard nonlinear bootstrap analysis, using an ad-hoc family of analytic and Gevrey‑$\gamma$ norms.
T.N. was a Visiting Fellow at Department of Mathematics, Princeton University, and partly supported by the NSF under grant DMS-1764119, an AMS Centennial fellowship, and a Simons fellowship.
I.R. is partially supported by the NSF grant DMS #1709270 and a Simons Investigator Award.
Received 4 July 2020
Accepted 14 December 2020
Published 29 August 2022