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 · Selected context
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.
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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 →