OpenAI · 371-01 · 2026-09-24 · Partial differential equations
Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus
preprints/Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026
Family 371. Stable blowup for a defocusing Schrödinger equation.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For a sufficiently large odd nonlinearity power, constructs a nonempty open set of initial data in , with , 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.
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.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 371: Stable blowup for the defocusing Schrödinger equation. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.