Unverified50% confidenceFactExact time
Any proof method that relies solely on abstract properties such as energy conservation and scaling analysis cannot prove the global regularity of the Navier-Stokes equation, because the averaged equation satisfies these properties yet still blows up.
1
Sources
50%
Confidence
Long-term
Relevance
9/12/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedSince the Navier–Stokes equations were proposed in the 19th century, the existence and smoothness of their solutions has remained unproven.73% similarUnverifiedThe Navier-Stokes problem involves the core proposition of global regularity for nonlinear equations in the theory of partial differential equations70% 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.66% similarUnverifiedThe existence and smoothness problem for the three-dimensional Navier-Stokes equations remains unsolved to this day.64% similarUnverifiedThe 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.62% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/914374API
curl https://kongchang.com/api/v1/knowledge/claims/914374MCP
get_claim(id=914374)