Tool Open source
NavierStokesAndEuler is an open-source Lean 4 formalization of results concerning finite-time breakdown in the Navier–Stokes and incompressible Euler equations, developed by OpenAI. For Navier–Stokes with positive viscosity, it formalizes constructions on both three-dimensional Euclidean space and the periodic torus using smooth initial data and external forcing; the results rule out global smooth solutions under the stated kinetic-energy or existence conditions. For the unforced Euler equations, it formalizes a smooth, compactly supported, divergence-free initial velocity whose solution develops a finite-time singularity, with the velocity’s C1 norm becoming unbounded and the time integral of the vorticity’s L-infinity norm diverging.
The repository uses Lean 4, Mathlib, and Lake. Its formalizations can be built after fetching the Mathlib cache, and the repository provides separate instructions for independently checking them with Comparator.
1 use taken from transcripts — each links to the moment in the video.
Publishes Lean formalizations and proofs concerning when smooth fluid motion breaks down, covering Navier–Stokes equations with external forcing and Euler equations without it. The repository includes instructions for independent checking.
1 in the library.