Asymptotic behavior of weak solutions to the damped Navier-Stokes equations

被引：5

作者：

Yu, Huan ^{[1
]}

Zheng, Xiaoxin ^{[2
]}

机构：

[1] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing 100192, Peoples R China

[2] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 477卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Asymptotic behavior; The damped Navier-Stokes equations; The nonlocal effect; LARGE TIME BEHAVIOR; L2; DECAY;

D O I：

10.1016/j.jmaa.2019.04.068

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Whether or not weak solutions of classical Navier-Stokes equations decay to zero in L-2 as time tends to infinity was posed by Leray in his pioneering paper [12,13] and has been well solved (see [15] for instance). This paper examines the three dimensional Navier-Stokes equations with damping term vertical bar u vertical bar(beta-1)u and proves that the weak solutions decay to zero in L-2 as time tends to infinity for any beta >= 1, by developing local-in-space estimate for weak solutions. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1009 / 1018

页数：10

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