%0 Journal Article
%T Two component regularity for the Navier-Stokes equations
%A Jishan Fan
%A Hongjun Gao
%J Electronic Journal of Differential Equations
%D 2009
%I Texas State University
%X 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 $ ablawidetilde{u}$ satisfy Serrin's type criterion.
%K Navier-Stokes equations
%K regularity criterion
%K two component
%K multiplier spaces
%K Besov spaces
%U http://ejde.math.txstate.edu/Volumes/2009/121/abstr.html