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Alpöge–Buckmaster: Boussinesq blowup with smooth forcing

Alpöge and Buckmaster report finite-time blowup for the inviscid Boussinesq equations on R² with smooth spatially compact forcing in both equations. Temperature remains bounded, while its gradient and the vorticity become unbounded.

Sources for this record

What was already known

The authors build on the multiscale program of Córdoba and Martínez-Zoroa and earlier Boussinesq work, extending the smooth-forcing construction.

What changed and why it matters

Establishes smooth-forcing breakdown for a central fluid-equation model and extends a method discussed as a route toward other regularity problems.

The AI contribution

The authors’ AI statement credits Claude and Codex iteration alongside human ideas, proof architecture, simplification and writing. Primary intellectual credit for the underlying strategy remains with earlier researchers.

Limitations

Forcing is essential to this statement. Tao’s explanation is an assessment of the ideas, not a complete independent proof check. The current manuscript was simplified after its first release; AIProofWatch reviewed its stated target and AI disclosure, not the full proof.

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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