I think it is relevant to note this proof is based on the incompressible Navier--Stokes equations. Real fluids are compressible. From the point of view of kin

I think it is relevant to note this proof is based on the incompressible Navier--Stokes equations. Real fluids are compressible. From the point of view of kinetic theory, even the compressible Navier--Stokes equations are only a first-order approximation to the Boltzmann equation. Further, many authors (including myself) have questioned whether the Chapman--Enskog approximation is justifiable for high Reynolds number flows. Certainly it is known that NS does not correctly describe shock flows, which are also high Reynolds number flows. I would say these papers represent an interesting mathematical exercise whose relevance to the physics of turbulence remains to be assessed.