Verified75% confidenceFactExact time
The two-dimensional version of the Navier-Stokes equations has been proven to have global smooth solutions, but the three-dimensional case remains unsolved due to the vorticity stretching mechanism.
3
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75%
Confidence
Long-term
Relevance
9/9/2026
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Related Claims
UnverifiedThe existence and smoothness problem for the three-dimensional Navier-Stokes equations remains unsolved to this day.77% similarVerifiedThe existence of smooth solutions to the Navier–Stokes equations in three-dimensional space has not yet been mathematically proven, and is one of the Millennium Prize Problems offered by the Clay Mathematics Institute.75% similarUnverifiedWhen viscosity is removed, the Navier-Stokes equations become the Euler equations.73% similarPartially VerifiedThe core question of the Navier-Stokes Millennium Prize Problem is: given smooth initial conditions in three-dimensional space, does the equation always have a global smooth solution?72% similarUnverifiedTerence Tao rigorously proved that solutions to the averaged version of the three-dimensional Navier-Stokes equation blow up in finite time.71% similar
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