On the interior regularity of suitable weak solutions to the Navier-Stokes equations

We obtain the interior regularity criteria for the vorticity of ``suitable'' weak solutions to the Navier-Stokes equations. We prove that if two components of a vorticiy belongs to $L^{q,p}_{t,x}$ in a neighborhood of an interior point with $3/p+2/q\leq 2$ and $3/2<p<\infty$, then solution is regular near that point. We also show that if the direction field of the vorticity is in some Triebel-Lizorkin spaces and the the vorticity magnitude satisfies an appropriate integrability condition in a neighborhood of a point, then solution is regular near that point.</p>