Theorem · version 1
In three space dimensions, the Navier–Stokes equations always have a weak solution (p, u) with suitable growth properties.
Weak solutions need not be smooth, and their uniqueness is not known.
Proved
Only the exact statement and source passage cited here; not an independent OpenMath assessment.
Existence and Smoothness of the Navier–Stokes Equation · p. 3, weak solutions (12)–(13) →
Observed Oct 21, 2026
In this problem · publication v8
Supporting result · Proved
Relationship not independently reviewed. This concerns its use in this problem.
Leray showed that the three-dimensional equations always have a weak solution with suitable growth properties; uniqueness of weak solutions is not known.
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 →