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 [image omitted] in a neighborhood of an interior point with 3/p+2/q2 and 3/2p, 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics