Theorem · version 1
Earlier version 1. View current version 2 →
For every ν > 0 there exist a smooth force compactly supported in ℝ³ × (0,∞), a fixed compact spatial set K, and smooth incompressible Navier–Stokes velocity and pressure on ℝ³ × [0,1), starting with u₀ = 0 and supported in K, such that kinetic energy stays uniformly bounded while limsup as t ↑ 1 of ‖u(t)‖∞ is infinite. Consequently no global smooth uniformly bounded-energy solution exists for the same data and force.
The manuscript gives this stronger explicit construction. The linked comparator nonexistence endpoint does not by itself formalize every property in this statement.
This source presents a theorem with a proposed proof. Its wording does not establish acceptance or independent mathematical review.
Proposed
Zero initial velocity; bounded energy and unbounded velocity before time one.
Finite Time Blowup for Navier–Stokes · Theorem 1.1; Corollary 10.6; Section 1.1 →
Source dated Sep 8, 2026 · Observed Oct 13, 2026
In this problem · publication v2 · Selected context
Supporting result · Proposed
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.
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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.
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Proposed
Zero initial velocity; bounded energy and unbounded velocity before time one.
Source dated Sep 8, 2026 · Observed Oct 13, 2026 · Source passage →