I think it is fair to say that any blowing-up solution of navier stokes would be of purely intellectual interest. NS is a problem that many smart people have thought about and failed to solve. The current picture is that there are probably self-similar blowing up solutions that exist at extremely high codimension in the space of initial conditions. Thus they are "probability zero", and, if essentially never arise in nature. (A nice analogy: imagine a movie of a stone falling into a pond, and the ripples created afterwards. Now run the movie of the ripples backwards. We never see this in nature!)