The Navier-Stokes existence and smoothness problem, a Clay Millennium Prize problem, remains unsolved as of 2026-10-02.

Is it true that the Navier-Stokes existence and smoothness problem, a Clay Millennium Prize problem, remains unsolved as of 2026-10-02?

Yes. Reference works state that the Navier-Stokes existence and smoothness problem is one of the Clay Millennium Prize Problems and remains unsolved, with a 2026 AI claim not independently verified. Attempted solutions in the record are unverified or retracted.

Verdict: SUPPORTED · 4 sources for, 4 against · Last checked 3 Oct 2026

The private library was unavailable for some searches in this check. Missing library results are not evidence against the claim.

Navier–Stokes existence and smoothness. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness

F, A. (2025). Global Smoothness and Existence for the Navier-Stokes Equations in Clay-ξ ↔ Format. doi.org. https://doi.org/10.22541/au.174664105.54119607/v1

Millennium Prize Problems. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Millennium_Prize_Problems

The Navier-Stokes problem in the 21st century. (2024). opac.k10plus.de. https://opac.k10plus.de/

Cody, M. A. (2025). Withdrawn: The Navier–Stokes Existence and Smoothness Problem: Motion is the Solution. doi.org. https://doi.org/10.20944/preprints202508.0243.v1

Martila, D. (2023). Navier—Stokes Millennium Prize problem is solved. doi.org. https://doi.org/10.32388/0k47t6

HS, D. (2022). No Existence and Smoothness of Solution of the Navier-Stokes Equation.. doi.org. https://doi.org/10.3390/e24030339

D, B., JM, L., & M, W. (2024). Twisting vortex lines regularize Navier-Stokes turbulence.. doi.org. https://doi.org/10.1126/sciadv.ado1969