Proved
Blowup from C^{1,α} data in ℝ³ (Elgindi 2021) ↗
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Theorem · version 1
Blowup from C^{1,α} data in ℝ³
Statement
For sufficiently small α > 0 there is a C^{1,α} axisymmetric velocity without swirl on ℝ³ whose incompressible Euler solution forms a singularity in finite time.
Assumptions
- Three-dimensional incompressible Euler equations.
- Reported in the 2026 manuscript’s historical context.
Scope
Data less regular than smooth; the smooth-data question in ℝ³ is not settled by it.
Evidence
Source reports
Connections
In this problem · publication v9 · Selected context
Three-dimensional Euler regularity →
Related result · Proved
A proved singularity in a nearby setting; the smooth unforced ℝ³ question differs.
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Finite Time Blowup for the Euler Equation →
- §1.1, Historical context; references [6], [7], [10], [15] → · Original passage ↗
Recorded wording
Elgindi (Annals 2021) proved finite-time blowup on ℝ³ for C^{1,α} axisymmetric velocities without swirl, for small α > 0. Córdoba and Martínez-Zoroa (2023) constructed finite-energy forced Euler solutions on ℝ³ that blow up. For smooth initial data, Chen and Hou (2022; rigorous numerics 2025) proved blowup in an axially periodic cylinder with an impermeable wall.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
OpenAI · Preprint · Publication date Sep 8, 2026
Revision & attribution
Source revision: 2026-09-08. Observed Oct 13, 2026.
OpenAI attributes the argument to its internal research model. Bibliographic authorship is printed as OpenAI; individual human preparation and checking roles are not inferred.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Blowup from C^{1,α} data in ℝ³ (Elgindi 2021) ↗
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026 · Source passage →
Record details
- Claim ID
- claim-euler-elgindi-c1alpha
- Statement version
- 1
- SHA-256
- 2f1be4091615ebedcdc32c82feb0689bf48dc9958f99fa03a8f4c2147cac6c24