论文标题
Landau阻尼用于分析和Gevrey数据
Landau damping for analytic and Gevrey data
论文作者
论文摘要
在本文中，我们给出一个基本证明，证明了penrose稳定平衡附近的弗拉索夫 - 波森系统的非线性降水，在圆环$ \ mathbb {t}^d \ times \ times \ times \ mathbb {r}^d $中首次获得了Mouhot和Villani在Mouhot和Villani中获得\ citry cite and \ cite cite and cite {mof citression {muhot citression and cite and cite {mot citression and cite＆citry cite {mv^c。 Masmoudi和Mouhot \ cite {bmm}用于Gevrey- $γ$数据，$γ\ in（\ frac13,1] $。我们的证明依赖于简单的分析估计和标准的非线性引导分析，使用分析和Gevrey-$ $ $ $ unds的标准非线性引导分析。
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 \cite{MV} for analytic data and subsequently extended by Bedrossian, Masmoudi, and Mouhot \cite{BMM} for Gevrey-$γ$ data, $γ\in(\frac13,1]$. 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.
