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OpenAI reports: Navier–Stokes blowup with smooth forcing

For every positive viscosity, the manuscript reports a three-dimensional incompressible Navier–Stokes flow starting from rest with smooth compactly supported forcing, bounded kinetic energy, and unbounded velocity in finite time. It claims Clay alternatives C on R³ and D on the periodic torus.

Sources for this record

What was already known

Earlier weak-solution nonuniqueness and rough-forcing constructions did not supply this smooth-forcing breakdown target.

What changed and why it matters

Settles the specified smooth-forcing breakdown alternatives of a Millennium Prize problem, despite leaving the unforced question separate.

The AI contribution

OpenAI attributes the construction to coordinated internal-model agents. The paper cites prior human work; concurrent Alpöge–Buckmaster work is separately credited.

Limitations

This is a forced result; unforced global regularity and real-world fluid prediction are separate questions. Clay’s 11 September announcement describes an apparent settlement, not a completed proof audit or prize award. AIProofWatch has not compiled the Lean project or checked the full proof. Priority and data-use disagreements are not adjudicated here.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The source reports this precise contribution; statement review does not establish a proof audit.

Accessible artifact / proof

Accessible supporting proof or code; not compiled or reproduced by AIProofWatch.

Correction and publication history

2026-10-11 · publication

Public-discussion audit found this substantive scoped contribution missing. Source statement, baseline, attribution and importance reviewed; no full proof audit. Historical addition without subscriber alerts.

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