Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 153, pp. 17.
Regularity for 3D NavierStokes equations
in terms of two components of the vorticity
Sadek Gala
Abstract:
We establish regularity conditions for the 3D
NavierStokes equation via two components of the vorticity vector.
It is known that if a LerayHopf weak solution
satisfies
where
form the two components of the vorticity,
, then
becomes the classical
solution on
(see [5]).
We prove the regularity
of LerayHopf weak solution
under each of the following
two (weaker) conditions:
where
is the
MorreyCampanato space.
Since
is a proper subspace of
, our regularity
criterion improves the results in ChaeChoe [5].
Submitted May 20, 2010. Published October 28, 2010.
Math Subject Classifications: 35Q35, 76C99.
Key Words: NavierStokes equations; regularity conditions;
MorreyCampaanto 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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