Spatially Quasi-Periodic Solutions of the Euler Equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-30 DOI:10.1007/s00021-023-00804-9

Xu Sun, Peter Topalov

引用次数: 0

Abstract

We develop a framework for studying quasi-periodic maps and diffeomorphisms on \({\mathbb {R}}^n\). As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on \({\mathbb {R}}^n\). In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.

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欧拉方程的空间拟周期解

我们开发了一个研究\({\mathbb {R}}^n\)上的拟周期映射和微分同态的框架。作为一个应用，我们证明了在\({\mathbb {R}}^n\)上准周期向量场空间中的欧拉方程是局部适定的。特别是，该方程保留了初始数据的空间准周期性。证明了解的解析依赖于时间和初始数据的几个结果。

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.