Stable blowup for the defocusing Schrödinger equation

For a sufficiently large odd nonlinearity power, constructs a nonempty open set of initial data in H^k(\mathbb T^{12}), 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)

Manuscript

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

September 24, 2026 · source · cite as \cite{OAI:Stable-Self-Similar-Blowup-for-a-Supercritical-Defocusing-Schrodinger-Equation-on-the-Torus-September-24-2026}

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.

Result 371 · Partial differential equations. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.