Open
Unforced periodic regularity target ↗
Alternative B; the selected forced construction does not settle this assertion.
Observed Oct 13, 2026
Conjecture · version 1
Unforced global regularity on the three-torus
Statement
For every ν > 0 and every smooth divergence-free periodic initial velocity, the unforced incompressible Navier–Stokes equations admit global smooth periodic velocity and pressure on ℝ³/ℤ³.
Assumptions
- Three-dimensional unit-periodic domain.
- Positive viscosity and no external force.
Scope
The official alternative B; a separate domain from whole-space regularity.
Evidence
Source reports
Connections
In this problem · publication v6 · Selected context
Navier–Stokes existence and smoothness →
Different statement · related variant · Open
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Navier–Stokes existence and smoothness →
Different statement · related variant · Open
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Existence and Smoothness of the Navier–Stokes Equation →
- Equations (1)–(9) and alternatives (A)–(D) → · Original passage ↗
Recorded wording
The official problem specifies alternatives A/B for unforced regularity and C/D for forced breakdown, with separate decay, periodicity and energy conditions.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Charles L. Fefferman · Published · Publication date 2000
Revision & attribution
Source revision: 2000. Observed Oct 13, 2026.
No specific AI contribution is attributed by this source record.
Finite Time Blowup for Navier–Stokes →
- Theorem 1.1; Corollary 10.6; Section 1.1 → · Original passage ↗
Recorded wording
The manuscript states forced breakdown from rest with compactly supported smooth forcing, bounded kinetic energy and unbounded velocity; it also states a periodic corollary.
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.
Open
Unforced periodic regularity target ↗
Alternative B; the selected forced construction does not settle this assertion.
Observed Oct 13, 2026 · Source passage →
Record details
- Claim ID
- claim-navier-stokes-unforced-periodic
- Statement version
- 1
- SHA-256
- 20f8a187edac5cc7ec0240dfaa41878f73776cffd3c2f4dd93e8096d392710c6