On nonlinear Landau damping and Gevrey regularity

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-06-14 DOI:10.1016/j.na.2025.113875

Christian Zillinger

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引用次数: 0

Abstract

In this article we study the problem of nonlinear Landau damping for the Vlasov–Poisson equations on the torus. We introduce anisotropic Gevrey spaces as a new tool to capture the time- and frequency-dependence of resonances. In particular, we show that for small initial data of size

0 < ϵ < ϵ_{0} (N)

and time intervals

(0, ϵ^{- N})

with

N \in N

arbitrary but fixed, nonlinear stability holds in regularity classes larger than Gevrey-3, uniformly in

ϵ

. As a complementary result we construct families of Sobolev regular initial data which exhibit nonlinear Landau damping. Our proof is based on the methods of Grenier, Nguyen and Rodnianski (Grenier et al., 2021).

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非线性朗道阻尼和格夫里正则性

本文研究环面上Vlasov-Poisson方程的非线性朗道阻尼问题。我们引入各向异性格夫里空间作为捕获共振的时间和频率依赖性的新工具。特别是，我们证明了对于大小为0<；ϵ<；ϵ0(N)的小初始数据和N∈N任意但固定的时间间隔（0,λ−N），非线性稳定性在大于gevry -3的正则类中保持一致，并且在λ中保持一致。作为补充结果，我们构造了具有非线性朗道阻尼的Sobolev正则初始数据族。我们的证明基于Grenier， Nguyen和Rodnianski （Grenier et al., 2021）的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

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