Blowup for supercritical nonlinear Schrodinger equations via concentration of an Euler front

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.

Leave a Reply

Your email address will not be published. Required fields are marked *