Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 148, pp. 1-6.
Title:A remark on the regularity for the 3D Navier-Stokes equations
in terms of the two components of the velocity
Author: Sadek Gala (Univ. of Mostaganem, Algeria)
Abstract:
In this note, we study the regularity of Leray-Hopf weak solutions
to the Navier-Stokes equation, with the condition
$$
\nabla (u_{1},u_{2},0)
\in L^{\frac{2}{1-r}}(0,T; \dot{\mathcal{M}}_{2,3/r} (\mathbb{R}^3) ,
$$
where $\dot{\mathcal{M}}_{2,3/r}(\mathbb{R}^3)$ is the
Morrey-Campanato space for $0