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

Chongsheng Cao

doi:10.3934/dcds.2010.26.1141

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2010, Volume 26, Issue 4: 1141-1151. Doi: 10.3934/dcds.2010.26.1141

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

Chongsheng Cao^1,

1.
Department of Mathematics, Florida International University, Miami, FL 33199

Received: December 2008

Revised: February 2009

Published: December 2010

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Abstract

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:

Three-dimensional Navier-Stokes equations,
Regularity criterion,
global regularity.

Mathematics Subject Classification: Primary: 35Q35, 65M70.

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