Theorem · version 1
In three space dimensions, assertions (A) and (B) hold provided the initial velocity satisfies a smallness condition.
Small data only; arbitrary large data remain open.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Existence and Smoothness of the Navier–Stokes Equation · p. 2, partial results: three dimensions →
Observed Oct 21, 2026
In this problem · publication v8 · Selected context
Special case · Proved
Scope: Global smooth solutions exist when the initial velocity is small.
Limit: Large initial data are not covered; the smallness threshold does not grow to all data.
A distinct scope, not an additive fraction of the problem solved.
Relationship not independently reviewed. This concerns its use in this problem.
In three dimensions, (A) and (B) hold provided the initial velocity satisfies a smallness condition.
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 →