Unverified50% confidenceFactExact time
The existence and smoothness problem for the three-dimensional Navier-Stokes equations remains unsolved to this day.
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50%
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Long-term
Relevance
9/11/2026
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Related Claims
UnverifiedThe 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.78% similarUnverifiedThe 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.77% similarUnverifiedSince the Navier–Stokes equations were proposed in the 19th century, the existence and smoothness of their solutions has remained unproven.76% 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?73% similarUnverified三体问题对任意初始条件都不存在通用的闭式解，庞加莱在19世纪末通过数学证明揭示了其不可积性69% similar
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