Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations
Terence Tao · blog · 2026-09-07 · ★★★★ · archived
Tao's exposition of the Alpöge–Buckmaster AI-assisted blow-up results, which appeared a day before OpenAI's Navier–Stokes claim and anchor the priority dispute.
Summary
Blog post by Terence Tao dated 7 Sep 2026 (US time; the Mastodon companion post is timestamped 8 Sep UTC). It explains Levent Alpöge and Tristan Buckmaster's proofs of finite-time blow-up with smooth forcing for 3D incompressible Euler, Boussinesq and the incompressible porous media equation. The work extends the Córdoba–Martínez-Zoroa scheme of iteratively adding localized high-frequency corrections that the low-frequency part amplifies exponentially. Tao notes the work was "heavily AI-assisted" and formalized in Lean. The authors had to release early because of "external events", meaning OpenAI's imminent Navier–Stokes announcement. Tao expects the method may extend to forced Navier–Stokes, which is what OpenAI then claimed its 10,000-agent run had proved. Checked via WebFetch.
Archived text
Page title: Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations
Page description: There’s some exciting very recent work by Alpöge and Buckmaster, building upon prior work by Córdoba and Martínez-Zoroa, in the general topic around the infamous global regularity problem for…
Metadata archived 2026-09-29; see Summary for content.
Related events
All posts · id: 2026-09-07-tao-finite-time-blowup-smooth-forcing