Verified90% confidenceFactExact time
The 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?
7
Sources
90%
Confidence
Long-term
Relevance
9/9/2026
First Seen
Sources
Related Entities
Related Claims
VerifiedThe 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.79% similarUnverifiedThe true Millennium Prize Problem refers to a universal proof of whether smooth solutions always exist for three-dimensional incompressible fluids under general conditions — a question that has neither been proven nor disproven to this day.74% similarUnverifiedThe core of the controversy focuses on the existence and smoothness problem of the Navier-Stokes equations73% similarUnverifiedThe existence and smoothness problem for the three-dimensional Navier-Stokes equations remains unsolved to this day.73% similarVerifiedThe 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.72% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/884285API
curl https://kongchang.com/api/v1/knowledge/claims/884285MCP
get_claim(id=884285)