UNIQUENESS OF BACKWARD ASYMPTOTICALLY ALMOST PERIODIC-IN-TIME SOLUTIONS TO NAVIER-STOKES EQUATIONS IN UNBOUNDED DOMAINS

摘要

We present a uniqueness theorem for backward asymptotically almost periodic solutions to the Navier-Stokes equations in 3-dimensional unbounded domains. 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(-∞,T; L_ω~3) within the class of solutions which have sufficiently small L∞(L_ω~3)-norm. In this paper, we show that a small backward asymptotically almost periodic solution in BC(-∞, T;L_ω~3∩L~（6,2）) is unique within the class of all backward asymptotically almost periodic solutions in BC(-∞, T;L_ω~3∩L~（6,2）).