Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains

被引：9

作者：

Farwig, Reinhard ^{[1
,2
]}

Taniuchi, Yasushi ^{[3
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany

[2] Ctr Smart Interfaces CSI, D-64287 Darmstadt, Germany

[3] Shinshu Univ, Dept Math Sci, Matsumoto, Nagano 3908621, Japan

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2011年 / 11卷 / 03期

关键词：

Navier-Stokes equations; Almost periodic solutions; Uniqueness; Unbounded domains; L2; DECAY; EXISTENCE; SYSTEM; STABILITY; FLOWS; SPACE;

D O I：

10.1007/s00028-010-0098-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a uniqueness theorem for almost periodic-in-time solutions to the Navier-Stokes equations in 3-dimensional unbounded domains. Thus far, uniqueness of almost periodic-in-time solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small almost periodic-in-time solution in BC(R; L-omega(3)) within the class of solutions that have sufficiently small L-infinity(L-omega(3))norm. In this paper, we show that a small almost periodic-in-time solution in BC(R; L-omega(3) boolean AND L-6,L-2) is unique within the class of all almost periodic-in-time solutions in BC(R; L-omega(3) boolean AND L-6,L-2). The proof of the present uniqueness theorem is based on the method of dual equations.

引用

页码：485 / 508

页数：24

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