Saint-Venant Estimates and Liouville-Type Theorems for the Stationary Navier–Stokes Equation in \(\mathbb {R}^3\)

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-08 DOI:10.1007/s00021-025-00941-3

Jeaheang Bang, Zhuolun Yang

引用次数: 0

Abstract

We prove two Liouville-type theorems for the stationary Navier–Stokes equations in \(\mathbb {R}^3\) under some assumptions on 1) the growth of the \(L^s\) mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.

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中平稳Navier-Stokes方程的Saint-Venant估计和liouville型定理 \(\mathbb {R}^3\)

我们证明了\(\mathbb {R}^3\)中平稳Navier-Stokes方程的两个liouville型定理，其条件是：(1)速度场的势函数的\(L^s\)平均振荡的增长，或(2)在无穷远处头压和速度场平方的相对衰减。主要思想是利用Saint-Venant型估计来表征非平凡解的狄利克雷能量的增长。这些假设比以前已知的类似性质的假设要弱。

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.