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

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics 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

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.