Uniqueness of Solutions on the Whole Time Axis to the Navier-Stokes Equations in Unbounded Domains

被引：7

作者：

Farwig, Reinhard ^{[1
,2
]}

Nakatsuka, Tomoyuki ^{[3
]}

Taniuchi, Yasushi ^{[4
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, Darmstadt, Germany

[2] Tech Univ Darmstadt, Int Res Training Grp Darmstadt Tokyo IRTG 1529, Darmstadt, Germany

[3] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648601, Japan

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

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 40卷 / 10期

基金：

日本学术振兴会;

关键词：

Almost periodic solutions; Mild solutions; Navier-Stokes equations; Precompact range condition; Unbounded domains; Uniqueness; 35Q30; 35A02; 76D05; PERIODIC-SOLUTIONS; MILD SOLUTIONS; NONSTATIONARY STOKES; L2; DECAY; FLOWS; EXISTENCE; SYSTEM; SEMIGROUP; STABILITY; BOUNDARY;

D O I：

10.1080/03605302.2015.1054938

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the uniqueness of bounded continuous L-3,L- -solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, L-p,L- q denotes the scale of Lorentz spaces. Thus far, uniqueness of such solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small solution in BC(; L-3,L- ) within the class of solutions which have sufficiently small L(L-3,L- )-norm. In this paper, we discuss another type of uniqueness theorem for solutions in BC(; L-3,L- ) using a smallness condition for one solution and a precompact range condition for the other one. The proof is based on the method of dual equations.

引用

页码：1884 / 1904

页数：21

共 47 条

[1]

[Anonymous], 1976, INTERPOLATION SPACES

[2] ALGEBRAIC L2 DECAY FOR NAVIER-STOKES FLOWS IN EXTERIOR DOMAINS [J].