  In this paper we study the incompressible Navier-Stokes equations in
$L^2(\mathbb R^3)\cap\mathcal X^{-1}(\mathbb R^3)$. In the global existence
case, we establish that if the solution $u$ is in the space $C(\mathbb
R^+,L^2\cap\mathcal X^{-1})$, then for $\sigma>-3/2$ the decay of
$\|u(t)\|_{\mathcal X^\sigma}$ is at least of the order of
$t^{-\frac{\sigma+\frac{3}{2}}{2}}$. Fourier analysis and standard techniques
are used.
