We prove that a weak solution u=(u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6,.
Bibliographical noteFunding Information:
This work was supported by the Korea Research Foundation Grant (MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00466).
All Science Journal Classification (ASJC) codes
- Applied Mathematics