Family 371Partial differential equationsNo LeanNot yet digested
Stable blowup for the defocusing Schrödinger equation
For a sufficiently large odd nonlinearity power, constructs a nonempty open set of initial data in , 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.
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Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus
Sep 24, 2026·paper.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.