PDE and mathematical physics · Sep 8, 2026
Forced three-dimensional Navier–Stokes singularity
OpenAI reports examples for every ν>0 in R³ and on the three-torus, under its specified forcing and initial-data conditions.
Scope and what remains
The force, decay, energy, domain and regularity assumptions are part of the question. This does not establish blowup for the unforced Navier–Stokes initial-value problem or prize acceptance.
Contributors
OpenAI internal research model for the mathematical argument; GPT-6 Astra for the later formalization workflow according to the announcement. Human checking and paper preparation are separate roles.
AI systems: GPT-6 Astra