Lebesgue和Morrey空间中平稳Navier-Stokes方程的若干Liouville定理

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-05-01 DOI:10.1016/j.anihpc.2020.08.006

Diego Chamorro , Oscar Jarrín , Pierre-Gilles Lemarié-Rieusset

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引用次数: 39

摘要

三维Navier-Stokes方程的Leray解的唯一性是一个具有挑战性的开放问题。在本文中，我们将研究在整个空间R3中的三维平稳Navier-Stokes方程的这个问题。在一些附加假设下，用Lebesgue和Morrey空间表述，我们将证明平凡解U→=0是唯一解。这类结果被称为刘维尔定理。

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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Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space $R^{3}$ . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution $\vec{U} = 0$ is the unique solution. This type of results are known as Liouville theorems.

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来源期刊

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.