  In this paper, we extend some results proved in previous references for
three-dimensional Navier-Stokes equations. We show that when the norm of the
velocity field is small enough in $L^3({I\!\!R}^3)$, then a global smooth
solution of the Navier-Stokes equations is ensured. We show that a similar
result holds when the norm of the velocity field is small enough in
$H^{\frac{1}{2}}({I\!\!R}^3)$. The scale invariance of these two norms is
discussed.
