平面稳态Navier-Stokes系统的基本速度估计及其应用

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-10 DOI:10.1007/s00021-025-00939-x

Mikhail Korobkov, Xiao Ren

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引用次数: 0

摘要

考虑平面域上一般稳定Navier-Stokes解的一些新的估计。根据我们的主要结果，如果域是凸的，那么在两个同心圆上的速度平均值之间的差是有界的（直到一个常数因子），由两个圆之间的环中的狄利克雷积分的平方根。这个不等式中的常数因子是普遍的，不依赖于圆半径的比值。讨论了这些公式的几种应用。

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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On Basic Velocity Estimates for the Plane Steady-State Navier–Stokes System and Its Applications

We consider some new estimates for general steady Navier–Stokes solutions in plane domains. According to our main result, if the domain is convex, then the difference between mean values of the velocity over two concentric circles is bounded (up to a constant factor) by the square-root of the Dirichlet integral in the annulus between the circles. The constant factor in this inequality is universal and does not depend on the ratio of the circle radii. Several applications of these formulas are discussed.

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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.