%0 Journal Article
%T On the role of $L^3$ and $H^{\frac{1}{2}}$ norms in hydrodynamics
%A Laurent Schoeffel
%J Physics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1412.6770v1