Theorem · version 1
In two space dimensions, the analogues of assertions (A) and (B) hold: smooth data lead to global smooth solutions with bounded energy. The same holds for the Euler equations.
A different dimension. The official description notes it gives no hint about three dimensions, where the main difficulties lie.
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: two dimensions →
Observed Oct 21, 2026
In this problem · publication v7 · Selected context
Different statement · related variant · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v8
Different statement · related variant · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In two dimensions the analogues of assertions (A) and (B) have long been known (Ladyzhenskaya), also for the Euler equations; the description notes this gives no hint about three dimensions.
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 →