Blow up dynamics for the 3D energy-critical nonlinear Schrödinger equation

Tobias Schmid (EPFL, Lausanne)

May 21. 2024, 14:00 — 15:00

We present a family of radial type II blow up solutions of the focusing quintic NLS in three dimensions which are obtained through renormalization of the ground state. The construction is based on an approximation scheme near the bulk solution which leads to a fast decaying error and is inspired by matched asymptotic heuristics. Further, we explain how to perturbatively obtain exact solutions using distorted Fourier techniques from the scattering data of the associated linearized 1D system, which has a resonance at zero energy threshold. If time permits, we comment on extensions of this method to the 4D cubic NLS and 4D Zakharov equation.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Nonlinear Waves and Relativity (Thematic Programme)
Organizer(s):
Roland Donninger (U of Vienna)
David Fajman (U of Vienna)
Birgit Schörkhuber (U of Innsbruck)