Existence of time-periodic strong solutions to the Navier-Stokes equation in the whole space

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-23 DOI:10.1016/j.jmaa.2024.128991

Tomoyuki Nakatsuka

引用次数: 0

Abstract

In this paper, the existence of time-periodic strong solutions to the Navier-Stokes equation in

R^{n}

is established under a suitable smallness condition on the external force. Our analysis is based on splitting periodic solutions into steady and purely periodic parts. One advantage of this decomposition is the availability of slightly more regularity in time of the purely periodic part. We apply this property to construct time-periodic solutions of the Navier-Stokes equation with information on the classes of their steady and purely periodic parts. It is also shown that the small solution v constructed in our existence theorem is unique within a class of time-periodic, not necessarily small, solutions having the same integrability properties as v.

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纳维-斯托克斯方程在整个空间中存在时周期强解

本文在外力的适当小度条件下，建立了 Rn 中纳维-斯托克斯方程的时间周期强解的存在性。我们的分析基于将周期解分割为稳定部分和纯周期部分。这种分解方法的一个优点是纯周期部分在时间上的规律性稍强。我们将这一特性应用于构建 Navier-Stokes 方程的时间周期解，并提供其稳定部分和纯周期部分的类别信息。我们还证明，在我们的存在定理中构建的小解 v 在一类时间周期解（不一定是小解）中是唯一的，该类解具有与 v 相同的可积分性。

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.