Finite time blowup for an averaged three-dimensional Navier-Stokes equation

Terence Tao has constructed a modified three-dimensional Navier-Stokes equation that exhibits finite-time blowup (solutions that become infinite in finite time) while satisfying the same function space estimates and energy identity as the true Navier-Stokes equations. This result formalizes the "supercriticality barrier," demonstrating that abstract mathematical approaches based solely on function space estimates and energy conservation cannot guarantee global regularity for the Navier-Stokes equation. The work suggests a potential pathway toward proving that the actual Navier-Stokes equations may also experience blowup for certain initial conditions.