Regularity Criterion for Solutions of Three-Dimensional Turbulent   Channel Flows
  In this paper we consider the three-dimensional Navier-Stokes equations in infinite channel. We provide a regularity criterion for solutions of the three-dimensional Navier-Stokes equations in terms of the vertical component of the velocity field. 
Chonsheng Cao, Junlin Qin and Edriss S. Titi