Unverified50% confidenceFactExact time
Terence Tao rigorously proved that solutions to the averaged version of the three-dimensional Navier-Stokes equation blow up in finite time.
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9/12/2026
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Related Claims
UnverifiedThe 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.71% similarUnverifiedTerence Tao suggests that if a similar self-replicating fluid machine could be constructed in the true three-dimensional Navier-Stokes equation, the answer to the Millennium Prize Problem would most likely be that blowup exists.65% similarUnverifiedThe existence and smoothness problem for the three-dimensional Navier-Stokes equations remains unsolved to this day.65% similarVerifiedAt the end of 2023, Terence Tao and collaborators used Lean and LLM assistance to prove an important special case of the polynomial Freiman-Ruzsa conjecture64% 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?63% similar
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