A solution to the focusing 3d NLS that blows up on a contracting sphere

Justin Holmer, Galina Perelman, Svetlana Roudenko

We rigorously construct radial $H^1$ solutions to the 3d cubic focusing NLS equation $i{\partial }_t\psi +\Delta \psi +2|\psi {|}^2\psi =0$ that blow-up along a contracting sphere. With blow-up time set…