Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 121, pp. 1-6.

Title: Two component regularity for the Navier-Stokes equations

Authors: Jishan Fan  (Nanjing Normal Univ., China)
         Hongjun Gao (Nanjing Normal Univ., China)

Abstract:         
 We consider the regularity of weak solutions to the Navier-Stokes
 equations in $\mathbb{R}^3$. Let $u:=(u_1,u_2,u_3)$ be a weak
 solution and $\widetilde{u}:=(u_1,u_2,0)$. We prove that $u$ is
 strong solution if $\nabla\widetilde{u}$ satisfy Serrin's type criterion.
 
Submitted August 28, 2009. Published September 29, 2009.
Math Subject Classifications: 35Q30, 35K15, 76D03.
Key Words: Navier-Stokes equations; regularity criterion;
           two component; multiplier spaces; Besov spaces.