Landau damping for analytic and Gevrey data

Emmanuel Grenier; Toan T. Nguyen; Igor Rodnianski

doi:10.4310/MRL.2021.V28.N6.A3

Landau damping for analytic and Gevrey data

Emmanuel Grenier, Toan T. Nguyen, Igor Rodnianski

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

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 T^d × 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-γ data, γ ∈ (¹₃ , 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.

Original language	American English
Pages (from-to)	1679-1702
Number of pages	24
Journal	Mathematical Research Letters
Volume	28
Issue number	6
DOIs	https://doi.org/10.4310/MRL.2021.V28.N6.A3
State	Published - 2021

ASJC Scopus subject areas

General Mathematics

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title = "Landau damping for analytic and Gevrey data",

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 Td × Rd that was first obtained by Mouhot and Villani in [9] for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot [2] for Gevrey-γ data, γ ∈ (13 , 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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T1 - Landau damping for analytic and Gevrey data

AU - Grenier, Emmanuel

AU - Nguyen, Toan T.

AU - Rodnianski, Igor

PY - 2021

Y1 - 2021

N2 - 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 Td × Rd that was first obtained by Mouhot and Villani in [9] for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot [2] for Gevrey-γ data, γ ∈ (13 , 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.

AB - 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 Td × Rd that was first obtained by Mouhot and Villani in [9] for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot [2] for Gevrey-γ data, γ ∈ (13 , 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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DO - 10.4310/MRL.2021.V28.N6.A3

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SP - 1679

EP - 1702

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 6

ER -

Landau damping for analytic and Gevrey data

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