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.
Bibliographical noteFunding Information:
This research is supported partially by KOSEF grant no. R01-2005-000-10077-0. D. Chae is supported by KRF Grant (MOEHRD, Basic Research Promotion Fund). K. Kang is supported by KRF-2006-331-C00020. J. Lee is supported by KRF-2006-311-C00007.
All Science Journal Classification (ASJC) codes
- Applied Mathematics