Global regularity or blowup of unforced 3D Navier-Stokes flows

Incompressible Navier-Stokes $\mathrm{d}u/\mathrm{d}t + (u.\mathrm{grad})u = \nu\,\mathrm{Lap}\,u - \mathrm{grad}\,p, \mathrm{div}\,u = 0$, on $R^3$ or the torus $T^3$ with $\nu > 0$, external force $f = 0$ and smooth divergence-free initial data (Schwartz class on $R^3$). Answer: a proof that the smooth solution exists for all $t > 0$ (Clay statements A and B), or smooth data whose solution has $\operatorname{limsup}_{t \to T} \mid\mid u(t)\mid\mid_{\infty} = \infty$ at a finite $T$.

A refereed, independently checked proof of global regularity or an explicit blowup construction with $f = 0$.