We establish regularity conditions for the 3D Navier-Stokes equation via two components of the vorticity vector. It is known that if a Leray-Hopf weak solution satisfies
where form the two components of the vorticity, , then becomes the classical solution on (see ). We prove the regularity of Leray-Hopf weak solution under each of the following two (weaker) conditions:
where is the Morrey-Campanato space. Since is a proper subspace of , our regularity criterion improves the results in Chae-Choe .
Submitted May 20, 2010. Published October 28, 2010.
Math Subject Classifications: 35Q35, 76C99.
Key Words: Navier-Stokes equations; regularity conditions; Morrey-Campaanto spaces.
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| Sadek Gala |
Department of Mathematics, University of Mostaganem
Box 227, Mostaganem 27000, Algeria
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