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The Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute's Millennium Prize Problems, has not been formally solved as of October 2026.

the verdict
SUPPORTED
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Recorded sources
2 sources for · 2 against

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Is it true that the Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute's Millennium Prize Problems, has not been formally solved as of October 2026?

Yes. Two reference sources state that as of 2026 (and specifically October 2026) the Navier-Stokes existence and smoothness problem remains unsolved and is considered active by the Clay Mathematics Institute, with only the Poincaré conjecture officially solved. Proposed solution papers and self-published claims exist but have not been formally verified or accepted.

Verdict: SUPPORTED · 2 sources for, 2 against · Last checked

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Evidence for · 2
Millennium Prize Problems
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Millennium Prize Problems. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Millennium_Prize_Problems

Evidence against · 2
Navier—Stokes Millennium Prize problem is solved
2023
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Martila, D. (2023). Navier—Stokes Millennium Prize problem is solved. doi.org. https://doi.org/10.32388/0k47t6

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More for · 1
Navier–Stokes existence and smoothness
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Navier–Stokes existence and smoothness. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness

More against · 1
A Short and Simple Solution of the Millennium Problem about the Navier-Stokes Equations and Similarly for the Euler Equations
2022
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A Short and Simple Solution of the Millennium Problem about the Navier-Stokes Equations and Similarly for the Euler Equations. (2022). hal.science. https://doi.org/10.4236/jamp.2022.108172

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