有限通道中一类单调剪切流的非线性不粘性阻尼 | 数学年鉴

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2024-05-01 DOI:10.4007/annals.2024.199.3.3

Nader Masmoudi, Weiren Zhao

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引用次数: 0

摘要

我们证明了一类单调剪切流在$\mathbb{T}\times [0,1]$中的非线性不粘性阻尼，其初始扰动为Gevrey-$\frac{1}{s}$类（$1\lt \frac{1}{s}<2$），具有紧凑支撑。证明的主要新思想是在一个精心选择的坐标系中构造并使用一个略微修正的瑞利算子的波算子。

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Nonlinear inviscid damping for a class of monotone shear flows in a finite channel | Annals of Mathematics

We prove the nonlinear inviscid damping for a class of monotone shear flows in $\mathbb{T}\times [0,1]$ for initial perturbation in Gevrey-$\frac{1}{s}$ class ($1\lt \frac{1}{s}<2$) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.