Finite time blowup with smooth forcing term for the incompressible porous medium
22 days ago
- Alpöge and Buckmaster, building on Córdoba and Martínez-Zoroa, demonstrated finite-time blowup for three model equations: the incompressible porous medium equation, the 2D Boussinesq equation, and the 3D incompressible Euler equations, with strong potential for extending to Navier-Stokes.
- The work is heavily AI-assisted and has been formalized in Lean, but the authors were forced to release preliminary preprints before full polishing due to external pressure from OpenAI.
- The strategy involves iteratively adding high-frequency corrections to a low-frequency solution, exploiting linearized instabilities to make the solution singular while keeping the forcing term smooth.
- OpenAI later announced an independent solution to the full Navier-Stokes problem, raising serious concerns about use of unpublished data, attribution, and ethical conduct in AI-driven mathematics.
- Tao emphasizes the importance of mathematical understanding over mere problem-solving, and calls for the community to uphold core values and reject irresponsible AI usage.