TY - JOUR
T1 - Landau damping for analytic and Gevrey data
AU - Grenier, Emmanuel
AU - Nguyen, Toan T.
AU - Rodnianski, Igor
N1 - 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.
UR - https://www.scopus.com/pages/publications/85116582016
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 -