A Priori Bounds for the Vorticity of Axis Symmetric Solutions to the   Navier-Stokes Equations
  We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations. 
Jennifer Burke and Qi S. Zhang