Uniqueness of Solutions on the Whole Time Axis to the Navier-Stokes Equations in Unbounded Domains |
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Authors: | Reinhard Farwig Tomoyuki Nakatsuka |
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Institution: | 1. Fachbereich Mathematik and International Research Training Group Darmstadt-Tokyo (IRTG 1529), Technische Universit?t Darmstadt, Darmstadt, Germany;2. Graduate School of Mathematics, Nagoya University, Nagoya, Japan |
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Abstract: | We consider the uniqueness of bounded continuous L3, ∞-solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, Lp, 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(?; L3, ∞) within the class of solutions which have sufficiently small L∞(L3, ∞)-norm. In this paper, we discuss another type of uniqueness theorem for solutions in BC(?; L3, ∞) 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. |
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Keywords: | Almost periodic solutions Mild solutions Navier-Stokes equations Precompact range condition Unbounded domains Uniqueness |
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