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

作者：Farwig Reinhard; Nakatsuka Tomoyuki; Taniuchi Yasushi^*

来源：Communications in Partial Differential Equations, 2015, 40(10): 1884-1904.

DOI：10.1080/03605302.2015.1054938

• Almost periodic solutions
• Mild solutions
• Navier-Stokes equations
• Precompact range condition
• Unbounded domains
• Uniqueness
• 35Q30
• 35A02
• 76D05

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.

• 出版日期2015-10-3