Ill-posedness for subcritical hyperdissipative Navier-Stokes equations   in the largest critical spaces
  We study the incompressible Navier-Stokes equations with a fractional Laplacian and prove the existence of discontinuous Leray-Hopf solutions in the largest critical space with arbitrarily small initial data. 
Alexey Cheskidov and Roman Shvydkoy
math.AP