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Navier-Stokes Existence and Smoothness

Millennium Prize Problem asking whether smooth solutions to the three-dimensional incompressible Navier-Stokes equations must stay smooth for all time or can break down in finite time, with official alternatives covering both three-dimensional space and the periodic torus.

Known aliases

Navier-Stokes problem

Relationships

No evidence-backed relationships are recorded.

Current clusters

build2 publishers

OpenAI ships a Lean build that checks its Navier-Stokes proof against its own definitions

OpenAI's 165-page proof ships with a Lean 4 formalization anyone can download and build, which settles whether the argument follows from its own definitions and leaves whether those definitions state the Clay problem to human readers.

Publishers:dev.toruntimewire.com

Reality

Evidence55
Adoption20
Hype gap+30
Incentives78
Confidence58