Electron. J. Diff. Equ., Vol. 2014 (2014), No. 232, pp. 1-12.

Remarks on regularity criteria for the 3D Navier-Stokes equations

Ruiying Wei, Yin Li

Abstract:
In this article, we study the regularity criteria for the 3D Navier-Stokes equations involving derivatives of the partial components of the velocity. It is proved that if $\nabla_{h}\widetilde{u}$ belongs to Triebel-Lizorkin space, $\nabla u_3$ or $ u_3$ belongs to Morrey-Campanato space, then the solution remains smooth on [0,T].

Submitted June 23, 2014. Published October 29, 2014.
Math Subject Classifications: 35Q35, 76D05.
Key Words: Regularity criteria; Triebel-Lizorkin space; Morrey-Campanato space.

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Ruiying Wei
School of Mathematics and Information Science
Shaoguan University
Shaoguan, Guangdong 512005, China
email: weiruiying521@163.com
Yin Li
School of Mathematics and Information Science
Shaoguan University
Shaoguan, Guangdong 512005, China
email: liyin2009521@163.com

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