Perhaps Navier Stokes can't be proved because it is impossible for laminar flow to
continue over a long time period.In this case we would have to show that
something equivalent to a Reynolds velocity applies to the system even when fluid moves below the Reynolds velocity threshold.This would have to be a kind of
distance threshold.But for distance to cause instability in the laminar flow,then
there must already be small imperfections in the laminar flow (which will evolve with time into turbulence) so that it isn't truly laminar.
The problem would then reduce to showing that there is in reality no such thing as a perfectly laminar flow.