openai/NavierStokesAndEuler

Lean certificates accompanying Navier-Stokes and Euler results

What it solves

This project provides formal mathematical proofs that certain solutions to the Navier-Stokes and Euler equations can "blow up" (develop singularities) in finite time. This addresses key alternatives of the Clay Mathematics Institute's Millennium Prize Problem regarding the existence and smoothness of Navier-Stokes solutions.

How it works

The project uses the Lean 4 interactive theorem prover to formalize the mathematical proofs presented in OpenAI's research papers. By translating the proofs into Lean 4 code, the project allows for independent, machine-verified verification of the complex mathematical results.

Who it’s for

This is intended for mathematicians, formal verification experts, and researchers interested in fluid dynamics and the formalization of high-level mathematics.

Highlights

  • Formalization of proofs for both the Navier-Stokes and Euler equations.
  • Addresses the breakdown of solutions in the whole space $\mathbb{R}^3$ and the periodic torus $\mathbb{R}^3/\mathbb{Z}^3$.
  • Demonstrates a singularity in finite time for unforced incompressible Euler equations.
  • Built using Lean 4, Mathlib, and Lake for independent proof checking.

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