Quasi-periodic Solutions for the Navier–Stokes Equation on Irrational Tori

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-16 DOI:10.1007/s00009-024-02727-9

Shangling Song

引用次数: 0

Abstract

This paper is concerned with the existence and stability of quasi-periodic solutions for the Navier–Stokes equation on irrational tori. We prove the persistence of quasi-periodic invariant tori under the small quasi-periodic external force. Furthermore, we obtain the orbital and asymptotic stability in the appropriate Sobolev space. Using the norm estimate of the heat propagator \(\textrm{e}^{t\Delta _{\alpha }}\), we get the solutions convergence exponentially to the invariant tori as \(t\rightarrow \infty \), with the rate of convergence \(O(\textrm{e}^{-\rho t})\) for any \(\rho \in (0,1)\).

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纳维-斯托克斯方程在无理环上的准周期解

本文关注纳维-斯托克斯方程在无理环上的准周期解的存在性和稳定性。我们证明了准周期不变环在小准周期外力作用下的持久性。此外，我们还获得了适当索波列夫空间中的轨道稳定性和渐近稳定性。利用热传播者的规范估计值（textrm{e}^{t\Delta _\alpha }}），我们得到解以指数形式收敛于不变环，即（t\rightarrow \infty \），收敛速率为（O(\textrm{e}^{-\rho t})），对于任意\(\rho \in (0,1)\)。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.