Theorem · version 1
If a classical solution of the Navier–Stokes equations on ℝ³ has finite maximal time of existence T*, then lim sup_{t→T*} ‖u(t)‖_{L³(ℝ³)} = +∞.
A blowup criterion; it does not say whether blowup occurs.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Tao · quantitative bounds for critically bounded solutions · p. 2, Theorem 1.1 →
Observed Oct 21, 2026
In this problem · publication v8
Conditional result · Proved
Scope: A solution whose critical L³ norm stays bounded cannot blow up.
Limit: Boundedness of the L³ norm is not known for general solutions.
A distinct scope, not an additive fraction of the problem solved.
Relationship not independently reviewed. This concerns its use in this problem.
Theorem 1.1, credited to Escauriaza–Seregin–Šverák: a classical solution with finite maximal time of existence has unbounded critical L³ norm as that time is approached.
paraphrase · No upstream full text is republished by this record.
Terence Tao · Published · Publication date Oct 14, 2021
Published in Proceedings of Symposia in Pure Mathematics 104 (2021), DOI 10.1090/pspum/104/01874. Statements here use the pinned arXiv v2: Theorem 1.1, which states the Escauriaza–Seregin–Šverák criterion.
Source revision: arxiv-v2. Observed Oct 21, 2026.
The cited work does not report AI involvement; absence of attribution is not evidence of absence.
Source updated Jul 10, 2020.
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
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026 · Source passage →