Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in R-3

We consider the regularity of weak solutions to the Navier-Stokes equations in R-3. Let u be a weak solution in R-3 x (0, T), w = curl u, and w = (w(1), w(2), 0). It is proved that u becomes a classical solution if w epsilon L-q (0, T; B(r)(0)sigma), for 2/q + 3/r = 2, 3/2 < r <= infinity, and sigma <= 2r/3. This is an improvement of the result given by Kozono-Yatsu [Extension criterion via two-components of vorticity on strong solution to the 3D Navier-Stokes equations, Math. Z. 246 (2003) 55-68]. (c) 2005 Elsevier Inc. All rights reserved.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000232086900007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)23ARTICLE2470-48121