Theorem · version 1
Let u be a weak solution of the Navier–Stokes equations satisfying suitable growth conditions, and let E be its singular set. Then the one-dimensional parabolic Hausdorff measure P¹(E) is zero. Such weak solutions exist for divergence-free initial data and force satisfying (4), (5).
The singular set cannot contain a spacetime curve, but singular points are not excluded.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Existence and Smoothness of the Navier–Stokes Equation · p. 4, Theorem (A), (B) →
Observed Oct 21, 2026
In this problem · publication v8
Bound · Proved
Scope: Possible singularities of suitable weak solutions form a set of zero one-dimensional parabolic measure.
Limit: This does not exclude singular points; it is the best partial regularity theorem known, and global smoothness remains open.
A distinct scope, not an additive fraction of the problem solved.
Relationship not independently reviewed. This concerns its use in this problem.
Caffarelli–Kohn–Nirenberg (simplified by Lin): the singular set E of a suitable weak solution has P¹(E) = 0, and such solutions exist for the given data.
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 →