Smooth or singular solutions to the Navier--Stokes system ?
  The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including stationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of pseudomeasure type. 
Marco Cannone and Grzegorz Karch