Terry Tao: Finite-time blowup breakthrough brings Navier-Stokes singularity within reach
Finite time blowup with smooth forcing term for the incompressible porous medium
Terry Tao reports on recent work by Alpöge and Buckmaster that demonstrates finite-time blowup with smooth forcing for three model fluid equations: the incompressible porous medium equation, the 2D Boussinesq equation, and the 3D incompressible Euler equations. The method iteratively adds high-frequency corrections to a low-frequency solution, exploiting instabilities in the linearized equation. Tao notes the work is heavily AI-assisted and formalized in Lean, and that extending it to Navier-Stokes now looks feasible.
Without such understanding, even a problem as infamous as the Navier-Stokes regularity problem of far less intrinsic significance to mathematics than is sometimes promoted in popular media.