We obtain a pointwise, a priori bound for the vorticity of axially symmetric solutions to the three-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 upper bound established for the axially symmetric Navier-Stokes equations.
"A priori bounds for the vorticity of axially symmetric solutions to the Navier-Stokes equations." Adv. Differential Equations 15 (5/6) 531 - 560, May/June 2010.