Finite-time Navier-Stokes blowup driven by a smooth force · revision history
Revision 1
Accepted · first revision · record
- Title
- Finite-time Navier-Stokes blowup driven by a smooth force
- Plain
- A machine-generated proof announced in September 2026 claims that a viscous fluid pushed by a smooth outside force can develop infinite velocity at one point in finite time. Whether the proof is correct decides two of the four official versions of the Clay problem.
- Precise
- For $\nu > 0$, do there exist smooth divergence-free u_0 with $\mid d^a u_0(x)\mid \le C_{a,K} (1+\mid x\mid)^{-K}$ and smooth f with $\mid d_x^a d_t^m f\mid \le C_{a,m,K} (1+\mid x\mid+t)^{-K}$ for which no smooth finite-energy solution of forced 3D Navier-Stokes exists on $R^3 x [0, \infty)$ (Clay statement C; statement D is the periodic version)? The OpenAI construction claims such a blowup; its structure, as abstracted by Constantin, Ignatova and Vicol (arXiv 2609.20803), is Type II with an anisotropic angular mean and exact axisymmetry in a core collapsing to the singular point. Answer: independent verification or a located error.
- Settled by
- A line-by-line check of the manuscript and of any accompanying formal proof, including a check that the formal definitions match the Clay statement.
- Kind
- well-posed
- Answer type
- yes-no
- References
- (empty)
- Literature status
- contested
- Status note
- Announced by OpenAI on 7-8 September 2026 (dates as reported by Petrillo and Glimm, arXiv 2609.23868); Constantin, Ignatova and Vicol (arXiv 2609.20803) proved rigidity constraints on constructions of its type; no independent verification as of 2026-10-01.
- Posed since
- 2000