On Isolated Singularities for the Stationary Navier–Stokes System

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2024-10-15 DOI:10.1007/s00021-024-00905-z

Alfonsina Tartaglione

引用次数: 0

Abstract

The classical problem of removable singularities is considered for solutions to the stationary Navier–Stokes system in dimension \(n\ge 3\) and an old theorem of Shapiro (TAMS 187:335–363, 1974) is recovered and extended to solutions in a half ball vanishing on the flat boundary. Moreover, for \(n=4\) it is proved that there are not distributional solutions, smooth away from the singularity and such that \(u(x)=O(|x|^{-1})\).

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关于静态纳维-斯托克斯系统的孤立奇点

对于维数 \(n\ge 3\) 的静态纳维-斯托克斯系统的解，考虑了可移动奇点的经典问题，恢复了夏皮罗（Shapiro）的一个老定理（TAMS 187:335-363, 1974），并扩展到在平边界上消失的半球中的解。此外，对于 \(n=4\)，证明了不存在分布解、远离奇点的平滑解以及 \(u(x)=O(|x|^{-1})\)。

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

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.