Long time decay for global solutions to the Navier-Stokes equations in Sobolev-Gevery spaces

Abstract

In this paper, we prove that if $u\in C([0,\infty ),{\dot{H}}_{a,1}^{1/2}({\mathbb{R}}^3))$ is a global solution of 3D incompressible Navier-Stokes equations, then $\Vert u{\Vert }_{{\dot{H}}_{a,1}^{1/2}}$ decays to zero as time approaches infinity. Fourier analysis and standard techniques are used.

14 pages