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1 correction found
Navier-Stokes has been solved with finite time blow ups at multiple labs
As of September 8, 2026, the Clay Mathematics Institute still lists the Navier–Stokes Millennium Prize problem as unsolved. There is no accepted proof establishing finite-time blow-up for the actual 3D Navier–Stokes equations.
Full reasoning
This claim is contradicted by the official status of the Navier–Stokes Millennium Prize problem.
The Clay Mathematics Institute — the organization that maintains the Millennium Prize Problems — currently labels the Navier-Stokes Equation page as "Unsolved" and states: "However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique?" That directly contradicts the statement that Navier–Stokes "has been solved."
Clay's current Unsolved archive also still includes Navier-Stokes Equation among the unsolved problems. If there were an accepted proof of finite-time blow-up for the actual 3D incompressible Navier–Stokes equations, this problem would not still be listed by Clay as unsolved.
There are papers on related models, special cases, and partial results, but those are not the same as a community-accepted solution to the Millennium Prize problem. As of September 8, 2026, the official record still says the problem remains unsolved.
2 sources
- Navier-Stokes Equation - Clay Mathematics Institute
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