Landau damping for analytic and Gevrey data

2020/04/13 by Grenier, Emmanuel, Nguyen, Toan T., Rodnianski, Igor · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2004.05979

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 \mathbbT^d × ℝ^d that was first obtained by Mouhot and Villani in \citeMV for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot \citeBMM for Gevrey-γ data, γ∈(\frac13,1]. Our proof relies on simple pointwise resolvent estimates and a standard nonlinear bootstrap analysis, using an ad-hoc family of analytic and Gevrey-γ norms.

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