open problem

Navier-Stokes Regularity

Whether smooth initial data for the 3D Navier-Stokes equations can develop singularities in finite time. A Clay Millennium Prize problem.

3 machine-reviewed papers whose extracted claims name this problem. Matching is literal, over the claim graph, so every listing traces to a sentence in a review.

This is the review hub: papers that name the problem, with the machine's verdict on each. The claims shelf lists the individual claims themselves, formal (Lean) or stated.

Share X Bluesky LinkedIn Reddit HN

ACCEPT An eps-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set
The upper box dimension of the interior singular set for suitable weak solutions of the 3D Navier-Stokes equations is bounded by 15/13.

arxiv:2610.17569 · math.AP · 2026-10
UNVERDICTED Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations
Suitable weak solutions of the incompressible MHD equations with external forces have singular sets of vanishing one-dimensional parabolic Hausdorff measure.

arxiv:2508.12317 · math.AP · 2025-08
UNVERDICTED Singularidades para as soluc{c}\~{o}es das Equac{c}\~{o}es de Navier-Stokes and Euler e o Problema do Mil\^(e)nio
An expert survey of the history, known theorems, and open status of singularity formation for the Navier-Stokes and Euler equations, with no new mathematical results.

arxiv:2509.07638 · math.AP · 2025-09