Terry Tao: finite-time smooth blowup proven for IPM, Boussinesq and Euler equations
alexisgallagher · x · 2026-09-10
Terry Tao blogged about a new breakthrough by Alpöge and Buckmaster, building on Córdoba and Martínez-Zoroa, toward the global regularity problem for incompressible 3D Navier-Stokes.
- It is now widely expected that smooth initial data and smooth forcing can make these equations develop finite-time singularities, possibly even without forcing.
- Alpöge and Buckmaster demonstrated finite-time blowup for three simpler model equations: the incompressible porous medium (IPM) equation, the 2D Boussinesq equation, and the 3D incompressible Euler equations.
- Their method very likely extends to Navier-Stokes itself, with completion feasible in the near future.
- The arguments have also been formalized in Lean, enabled by modern autoformalization agents.
Related event: Tao Hails AI-Assisted Fluid Blowup Breakthrough, Formalized in Lean(9 posts)→
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