A new regularity criterion for weak solutions to the Navier-Stokes equations

In this paper we obtain a new regularity criterion for weak solutions to the 3-D Navier-Stokes equations. We show that if any one component of the velocity field belongs to L-alpha ([0, T); L-gamma (R-3)) with 2/alpha + 3/gamma <= 1/2, 6 < gamma <= infinity, then the weak solution actually is regular and unique. (c) 2005 Elsevier SAS. All rights reserved.