Smoothness vs Wellposedness vs Clay Problem vs Ghost Solutions

The official Clay Navier-Stokes Prize Problem asks about existence of smooth solutions but does not mention uniqueness or wellposedness as continuous dependence of the solution on data. This is because in the standard mathematical analysis of differential equations, uniqueness/wellposedness is viewed to be a byproduct of proving smoothness through bounds of derivatives of the solution in terms of data.

Asking for smooth solutions in the Clay Problem thus is viewed to include uniqueness without specific mention. But this opens an ambiguity by allowing the continuous dependence to include Lipschtiz or continuity constants of any size. This opens to viewing a turbulent solution with very large derivatives as a smooth solution with very large Lipschitz constants effectively eroding the very meaning of continuous dependence.

The true nature of turbulent flow is non-smooth with continuous dependence of mean values but not point values, thus exhibiting a form of weak wellposedness allowing meanvalues such as drag and lift to be computed as well determined quantities with continuous dependence on data. 

The official formulation by Fefferman as leading mathematical analyst thus reflects a form of mathematical analysis, which misses the main character of the Navier-Stokes equations with small vanishing viscosity as having turbulent solutions, which are non-smooth without singularities, thus falling outside the Fefferman formulation. 

Fefferman's mistake was to set viscosity to unity for a problem with small/vanishing viscosity as essence. In a math test that would give an F enforced by the fact that the Euler equation with zero viscosity is mentioned in the same breath as Navier-Stokes. The Clay problem debacle shows the effect of separating math from physics in a problem with physics origin. 

The Clay problem thus needs a reformulation bringing in the turbulence very clearly expressed as motivation, but then forgotten. Without reformulation the problem will continue to direct major efforts into capturing solutions of no interest, with the recent OpenAI solution now shown by Constantin et al to be a ghost solution.