Abstract
We present a uniqueness theorem for time-periodic solutions to the Navier–Stokes equations in unbounded domains. Thus far, results on the uniqueness of time-periodic solutions to the Navier–Stokes equations in unbounded domain, roughly speaking, have only found that a small time-periodic Ln-solution is unique within the class of solutions which have sufficiently small L∞(Ln)-norm. In this paper, we show that a small time-periodic Ln-solution is unique within the class of all time-periodic Ln-solutions, which contains large solutions. We also consider the uniqueness of solutions in weak-Ln space. The proof of the present uniqueness theorem is based on the method of dual equations.
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