Theorem · version 1
If a smooth velocity field on ℝ³ × [0,T) is supported in one fixed compact spatial set and its spatial supremum norm has infinite limsup as t ↑ T < ∞, then it has no smooth continuation to ℝ³ × [0,∞) that agrees with it before T.
A conditional consequence of continuity on a compact space-time set; it does not certify existence of a singular Navier–Stokes solution.
Proved
Conditional compact-support argument; not an assessment that the constructed witness is correct.
Finite Time Blowup for Navier–Stokes · Theorem 1.1; Corollary 10.6; Section 1.1 →
Observed Oct 13, 2026
In this problem · publication v3 · Selected context
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
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
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.
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Conditional compact-support argument; not an assessment that the constructed witness is correct.
Observed Oct 13, 2026 · Source passage →