A remark on Liouville-type theorems for the stationary Navier-Stokes equations in three space dimensions

被引：75

作者：

Kozono, Hideo ^{[1
]}

Terasawa, Yutaka ^{[2
]}

Wakasugi, Yuta ^{[2
]}

机构：

[1] Waseda Univ, Fac Sci & Engn, Dept Math, Tokyo 1698555, Japan

[2] Nagoya Univ, Grad Sch Math, Chikusa Ku, Furocho, Nagoya, Aichi 4648602, Japan

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 272卷 / 02期

关键词：

Navier-Stokes equations; Finite Dirichlet integral; Scaling invariance; Liouville-type theorem;

D O I：

10.1016/j.jfa.2016.06.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the 3D homogeneous stationary Navier-Stokes equations in the whole space R-3 We deal with solutions vanishing at infinity in the class of the fmite Dirichlet integral. By means of quantities having the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application, we prove the Liouville theorem in the marginal case of scaling invariance. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：804 / 818

页数：15

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