# American Institute of Mathematical Sciences

October  2010, 26(4): 1141-1151. doi: 10.3934/dcds.2010.26.1141

## Sufficient conditions for the regularity to the 3D Navier-Stokes equations

 1 Department of Mathematics, Florida International University, Miami, FL 33199, United States

Received  December 2008 Revised  February 2009 Published  December 2009

In this paper we consider the three-dimensional Navier-Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one direction derivative of the velocity field, namely, $u_z$, for the regularity of strong solutions to the three-dimensional Navier-Stokes equations.
Citation: Chongsheng Cao. Sufficient conditions for the regularity to the 3D Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1141-1151. doi: 10.3934/dcds.2010.26.1141
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