openai/NavierStokesAndEuler

Lean certificates accompanying Navier-Stokes and Euler results

What it solves

This project provides formal mathematical proofs that 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 proofs are implemented as formalizations in the Lean 4 theorem prover. By encoding the mathematical results into Lean, the proofs can be be independently verified by a computer to ensure absolute correctness.

Who it’s for

Researchers in mathematics, fluid dynamics, and formal verification who want to examine or verify the proofs of finite-time blowup for these fundamental physics equations.

Highlights

  • Formalized proofs for Navier-Stokes equations in both whole space ($\mathbb{R}^3$) and periodic torus ($\mathbb{R}^3/\mathbb{Z}^3$).
  • Formalized proof for the unforced incompressible Euler equations showing a singularity develops in finite time.
  • Built using Lean 4 and Mathlib for rigorous computer-verified mathematics.

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