Proved
Blowup with external forcing (Córdoba & Martínez-Zoroa 2023) ↗
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Theorem · version 1
Blowup with external forcing
Statement
There are finite-energy solutions of the forced incompressible Euler equations on ℝ³, with velocity in C^{3,1/2} before blowup and a force uniformly bounded in C^{1,1/2−ε} ∩ L², that form a singularity in finite time.
Assumptions
- Three-dimensional incompressible Euler equations.
- Reported in the 2026 manuscript’s historical context.
Scope
A force is applied; the question asks about unforced evolution.
Evidence
Source reports
Connections
In this problem · publication v9
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 with external forcing (Córdoba & Martínez-Zoroa 2023) ↗
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-forced-blowup
- Statement version
- 1
- SHA-256
- 3baf27f97c06979d352a9a879adb33d6b2c146583ed0ba81a0dc1359cdbcc2ae