The HADES seminar on Tuesday, September 8will be given by James Rowan via Zoom (please contact the organizer at “james_rowan at berkeley dot edu” for the Zoom ID) from 3:40 to 5 pm.
Speaker: James Rowan
Abstract: I will present a recent paper by Merle, Raphael, Rodnianski, and Szeftel which constructs a new kind of blowup solution for certain supercritical nonlinear Schrodinger equations. The mechanism is neither a rapid frequency cascade nor concentration of a [quasi]soliton, but rather a highly-oscillatory front blowup coming from a collection of special solutions to the self-similar spherically symmetric Euler equations. The construction relies on studying the behavior of a wave equation in the phase and modulus variables and a fixed point argument to control the behavior of unstable modes. Along the way I hope to showcase some common techniques in the study of nonlinear PDEs.