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-t,x(q,p) in a neighborhood of an interior point with 3/p + 2/q <= 2 and 3/2 < p < infinity, 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 vorticity magnitude satisfies an appropriate integrability condition in a neighborhood of a point, then solution is regular near that point.