No Verified Proof Yet for Global Regularity or Blow‑Up in 3‑D Navier‑Stokes Despite Recent AI‑Generated Estimates — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Recent public AI‑generated content and pre‑print claims propose novel a‑priori estimates for the 3‑D incompressible Navier‑Stokes system, but no peer‑reviewed proof of global regularity or finite‑time blow‑up has been verified. | MATH: Navier‑Stokes (inviscid density ρ=1) \[ \partial_t u + (u\!\cdot\!\nabla)u = -\nabla p + \nu\Delta u,\qquad \nabla\!\cdot u =0, \] Key proposed estimate (arXiv 1806.10081v10): \[ \|u(t)\|_{H^1}^2 + \nu\int_0^t\|\Delta u(s)\|_{L^2}^2\,ds \le C\bigl(\|u_0\|_{H^1}^2\bigr)\exp\!\bigl(K\int_0^t\|u(s)\|_{L^\infty}\,ds\bigr), \] with claimed bound \(\int_0^T\|u\|_{L^\infty}\,ds\le C\,T^{\alpha}\) for \(\alpha<1\). | CONNECTION: No explicit golden‑ratio or base‑60 constants appear in the presented estimates. The only implicit geometric structure is the underlying \(SO(3)\) rotational symmetry of the equations and the energy‑enstrophy cascade hierarchy, which can be represented on a dyadic lattice whose scaling exponent \(\frac{5}{3}\) (Kolmogoro Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225458778