Sadek Gala
Abstract:
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 [5]).
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 [5].
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 email: sadek.gala@gmail.com |
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