Existence and stability of corotational wave maps into perturbed spheres

Alexander Wittenstein (KIT, Karlsruhe)

Jun 18. 2024, 15:30 — 15:45

In this talk we will be considering corotational, energy-supercritical wave maps from Minkowski space into target manifolds which are geometrically close to a sphere. It is already known that if the target manifold is precisely a sphere, the wave maps model exhibits explicitly known self-similar blowup solutions, which are asymptotically nonlinear stable against small perturbations.
Using perturbative methods we show that there do not only exist self-similar solutions to the wave maps equation when the target manifold is a perturbed sphere but that they are also asymptotically nonlinear stable.

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)