Global Regular Axially-Symmetric Solutions to the Navier–Stokes Equations with Small Swirl

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-08-04 DOI:10.1007/s00021-023-00793-9

Bernard Nowakowski, Wojciech M. Zajaczkowski

引用次数: 0

Abstract

Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.

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具有小旋流的Navier-Stokes方程的全局正则轴对称解

研究了有界圆柱体中Navier-Stokes方程的轴对称解。在边界上，假设速度的法向分量和速度和涡量的角分量消失。如果初始旋流范数足够小，则显示出轴对称弱解的规律性。关键工具是对某些加权Sobolev空间中的流函数进行新的估计。

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.