Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations

In this paper we prove, if $u\in\mathcal C([0,\infty),{\bf {\mathcal X}^{-1}}(\mathbb R^3))$isglobalsolutionof3DNavier-Stokesequations,then$|u(t)|_{{\bf {\mathcal X}^{-1}}}$ decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.