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.