Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains

作者：Farwig Reinhard^*; Taniuchi Yasushi

来源：Journal of Evolution Equations, 2011, 11(3): 485-508.

DOI：10.1007/s00028-010-0098-3

• Navier-Stokes equations
• Almost periodic solutions
• Uniqueness
• Unbounded domains

We present a uniqueness theorem for almost periodic-in-time solutions to the Navier-Stokes equations in 3-dimensional unbounded domains. Thus far, uniqueness of almost periodic-in-time solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small almost periodic-in-time solution in BC(R; L(omega)(3)) within the class of solutions that have sufficiently small L(infinity)(L(omega)(3))norm. In this paper, we show that a small almost periodic-in-time solution in BC(R; L(omega)(3) boolean AND L(6,2)) is unique within the class of all almost periodic-in-time solutions in BC(R; L(omega)(3) boolean AND L(6,2)). The proof of the present uniqueness theorem is based on the method of dual equations.

• 出版日期2011-9