Theorem · version 1
For initial data not assumed small, assertions (A) and (B) hold, also for ν = 0, on a time interval [0, T) with T depending on the initial data. For ν > 0, if the maximal time of existence is finite, the velocity becomes unbounded near it.
Short time only; whether the maximal time can be finite is the open question.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Existence and Smoothness of the Navier–Stokes Equation · pp. 2–3, blowup time →
Observed Oct 21, 2026
In this problem · publication v7 · Selected context
Special case · Proved
Scope: Every smooth initial velocity has a smooth solution on a short time interval.
Limit: Whether this interval can always be extended to all time is exactly the problem.
A distinct scope, not an additive fraction of the problem solved.
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Special case · Proved
Scope: Every smooth initial velocity has a smooth solution on a short time interval.
Limit: Whether this interval can always be extended to all time is exactly the problem.
A distinct scope, not an additive fraction of the problem solved.
Relationship not independently reviewed. This concerns its use in this problem.
For data not assumed small, (A) and (B) hold on a short time interval depending on the data; for ν > 0 a finite blowup time forces the velocity to become unbounded.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Charles L. Fefferman · Published · Publication date 2000
Source revision: 2000. Observed Oct 13, 2026.
No specific AI contribution is attributed by this source record.
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 →