Partial Regularity for the Steady Fractional Navier-Stokes Equations in Dimension \(\mathbf{{n}}\)

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-18 DOI:10.1007/s00021-025-00952-0

Jiaqi Yang

引用次数: 0

Abstract

In this paper, we study weak solutions to the steady (time-independent) fractional Navier-Stokes system in \(\mathbb {R}^n\). We offer a novel perspective to study the partial regularity of steady problem, and show that if \(\alpha \in (\frac{n+1}{6},\frac{n+2}{6})\), the Hausdorff dimension of singular set for the steady weak solution is at most \(n+2-6\alpha \). Our approach is inspired by the ideas of Katz and Pavlović (Geom. Funct. Anal. 12:2 (2002), 355-379) and Ożański (Anal. PDE 16:3 (2023)). This is the first attempt to apply the method of Katz and Pavlović to a steady setting.

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稳定分数阶Navier-Stokes方程的部分正则性 \(\mathbf{{n}}\)

本文研究了\(\mathbb {R}^n\)中稳定（时间无关）分数阶Navier-Stokes系统的弱解。我们提供了一个新的视角来研究稳定问题的部分正则性，并证明了当\(\alpha \in (\frac{n+1}{6},\frac{n+2}{6})\)时，稳定弱解的奇异集的Hausdorff维数最多为\(n+2-6\alpha \)。我们的方法受到Katz和pavloviki （Geom）思想的启发。函数。肛门。12:2(2002),355-379)和Ożański(肛门。Pde 16:3(2023))。这是将卡茨和巴甫洛维奇的方法应用于稳定环境的第一次尝试。

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.