On weighted-norm estimates for nonstationary incompressible Navier-Stokes flows in a 3D exterior domain

被引：20

作者：

He, Cheng ^{[1
]}

Miyakawa, Tetsuro ^{[2
]}

机构：

[1] Chinese Acad Sci, Inst Appl Math Acad Math & Syst Sci, Beijing 100080, Peoples R China

[2] Kanazawa Univ, Div Math & Phys, Kanazawa, Ishikawa 9201192, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 246卷 / 06期

基金：

日本学术振兴会;

关键词：

Navier-Stokes equations; Exterior problem; Weighted estimates; Total net force; WEAK SOLUTIONS; ASYMPTOTIC-BEHAVIOR; ROTATIONAL SYMMETRIES; EQUATIONS; DECAY; SPACES; STATIONARY; PROFILES; ENERGY; LR;

D O I：

10.1016/j.jde.2008.09.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the time-decay of weighted norms of weak and strong solutions to the Navier-Stokes equations in a 3D exterior domain. Moment estimates for weak solutions and weighted L(q)-estimates for strong solutions are deduced, both of which seem to be optimal. The relation is discussed between the space-time decay and the vanishing of the total net force exerted by the fluid to the body. A class of initial data is given so that the total net force associated to the corresponding fluid flows does not vanish. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：2355 / 2386

页数：32

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