On boundedness, existence and uniqueness of strong solutions of the   Navier-Stokes Equations in 3 dimensions
  In this paper we consider the Navier-Stokes Equations in 3 dimensions in the vorticity formulation in the absence of the external forces. We derive upper bounds on L_{infinity} norm of omega and use them together with the Local Existence and Uniqueness results to show Global Existence and Uniqueness of the solution provided that at t=0, L_{infinity} norm of omega is finite, or L_4 norm of omega is finite. 
A. A. Ruzmaikina