For arbitrarily large odd nonlinear powers, some Sobolev index k>8 admits a nonempty open set of Hᵏ initial data on the twelve-dimensional torus whose defocusing nonlinear Schrödinger solutions undergo classical finite-time self-similar blowup.
For arbitrarily large odd nonlinear powers, some Sobolev index k>8 admits a nonempty open set of Hᵏ initial data on the twelve-dimensional torus whose defocusing nonlinear Schrödinger solutions undergo classical finite-time self-similar blowup.
For arbitrarily large odd nonlinear powers, some Sobolev index k>8 admits a nonempty open set of Hᵏ initial data on the twelve-dimensional torus whose defocusing nonlinear Schrödinger solutions undergo classical finite-time self-similar blowup.
If correct, gives stable finite-time blowup in a defocusing energy-supercritical nonlinear Schrödinger equation.
Can high-regularity open sets of data blow up for a defocusing supercritical Schrödinger equation?
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OpenAI reports stable blowup for defocusing Schrödinger flow on a torus
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