TY - JOUR
T1 - Landau damping for analytic and Gevrey data
AU - Grenier, Emmanuel
AU - Nguyen, Toan T.
AU - Rodnianski, Igor
N1 - Funding Information:
TN 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. IR is partially supported by the NSF grant DMS #1709270 and a Simons Investigator Award.
Publisher Copyright:
© 2021 International Press of Boston, Inc.. All rights reserved.
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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U2 - 10.4310/MRL.2021.V28.N6.A3
DO - 10.4310/MRL.2021.V28.N6.A3
M3 - Article
AN - SCOPUS:85116582016
SN - 1073-2780
VL - 28
SP - 1679
EP - 1702
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 6
ER -