Open problems concerning the Holder continuity of the direction of   vorticity for the Navier-Stokes equations
  In these notes we consider solutions u to the evolution three dimensional Navier-Stokes equations in the whole space. Set w= curl u, the vorticity of u. Our study concerns mainly the relation between Holdercontinuity assumptions on the direction of the vorticity and induced space-time integrability regularity results for w. We discuss some related open problems, consistent with our calculations. We hope that our approach should help readers interesting in carrying on the investigation. 
Hugo Beirao da Veiga
math.AP