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
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
收藏
页码:2355 / 2386
页数:32
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