AI BriefingNavierStokesAndEuler: Navier-Stokes Finite Time Blowup, Mathematically Proven and Verified in Lean 4
openai/NavierStokesAndEuler
About the project
This repository formalizes the finite time blowup phenomenon of the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Prize Problems, in Lean 4. It implements the mathematical results proposed by OpenAI as Lean 4 code, which is mechanically verifiable, thereby eliminating the possibility of logical errors.
It proves that no global smooth solutions exist when the viscosity coefficient is positive in the whole space R^3 and the periodic torus R^3/Z^3. For the incompressible Euler equations, it includes the process by which an initial velocity field that is smooth and has compact support in R^3 forms a singularity in finite time.
It supports independent proof verification using Mathlib and the Lake build system. It provides a case study of computers directly verifying complex fluid dynamics theory for researchers who prioritize mathematical rigor or developers interested in formal proofs.
openai/NavierStokesAndEuler
Lean certificates accompanying Navier-Stokes and Euler results
Lean
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