Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations

We consider the regularity criteria for a weak solution u = (u(1), u(2), u(3)) to the Navier-Stokes equations in R-3. Denoting by omega = (omega(1), omega(2), omega(3)) = curl u the vorticity, we then prove that u is smooth, provided u(3), omega(3); or partial derivative(3)u(3), omega(3) are in some Serrin-type integrability classes. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589966]