openai/NavierStokesAndEuler
Lean certificates accompanying Navier-Stokes and Euler results
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This repository contains Lean 4 formalizations of the results presented in “Finite time blowup for Navier–Stokes” and “Finite time blowup for the Euler equation” by OpenAI. For every positive viscosity, we prove two results: which no global smooth solution with uniformly bounded kinetic energy exists. initial data and forcing for which no global smooth solution exists. These are alternatives (C) “Breakdown of Navier–Stokes solutions on ℝ³” and (D) “Breakdown of Navier–Stokes Solutions on ℝ³/ℤ³” in the Clay Mathematics Institute’s official problem description of the Navier–Stokes existence and smoothness Millennium Prize Problem. We construct smooth, compactly supported, divergence-free initial velocity…
Read the full README ↗ · Preview checked 2026-10-31T19:50:30.529Z
Inside the original README — Document outline
- Finite time blowup for Navier–Stokes and Euler equations
- Navier Stokes
- Euler
- Building the formalizations
- Independent proof checking
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What this repository does
Lean certificates accompanying Navier-Stokes and Euler results
Repository facts
- Owner
- openai
- Primary language
- Lean
- Stars
- 2,053
- Forks
- 215
- Open issues + pull requests
- 0
- License
- Apache-2.0
- Archived
- No
- Default branch
- main
- Created
- 2026-09-08T10:53:38.000Z
- Last push
- 2026-09-10T15:14:13.000Z
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