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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.

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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.

Why it matters

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

What counts as progress

A sourced result with the exact hypotheses, baseline, and AI role stated; verification is assessed separately.

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  • Compare the precise theorem and hypotheses with the previous baseline.
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Background review: 2026-10-11. Selected sources:

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