Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 06, pp. 1-7.
Title: A regularity criterion for the Navier-Stokes equations in terms
of the horizontal derivatives of the two velocity components
Authors: Wenying Chen (Chongqing Three Gorges Univ., China)
Sadek Gala (Univ. of Mostaganem, Algeria)
Abstract:
In this article, we consider the regularity for weak solutions
to the Navier-Stokes equations in $\mathbb{R}^3$.
It is proved that if the horizontal derivatives of the two
velocity components
$$
\nabla _h\widetilde{u}\in L^{2/(2-r)}(0,T;\dot{\mathcal{M}}_{2,3/r}
(\mathbb{R}^3)),\quad \hbox{for }0