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

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