Stable blowup for the defocusing Schrödinger equation

What OpenAI claims

For a sufficiently large odd nonlinearity power, constructs a nonempty open set of initial data in H^k(𝕋¹²), with k > 8, whose solutions of the scalar defocusing nonlinear Schrödinger equation blow up in finite time. Thus finite-time blowup is stable under Sobolev perturbations in this supercritical regime. (Lean)

Paper

1. Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove stable self-similar finite-time blowup for a supercritical defocusing nonlinear Schrödinger equation on the twelve-dimensional torus. For a sufficiently large odd power, the blowup initial data contain a nonempty open set in a high Sobolev space. As a consequence, Gaussian Fourier initial data of arbitrarily high Sobolev regularity can have positive probability of finite-time blowup.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.