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

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

Chongsheng Cao 1,

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.
Keywords: global regularity., Three-dimensional Navier-Stokes equations, Regularity criterion.
Mathematics Subject Classification: Primary: 35Q35, 65M7.
Citation: Chongsheng Cao. Sufficient conditions for the regularity to the 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1141-1151. doi: 10.3934/dcds.2010.26.1141
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