Existence and Stability of Corotational Wave Maps into Perturbed Spheres

Explore corotational, energy-supercritical wave maps from Minkowski space into target manifolds geometrically close to a sphere in this 13-minute conference talk. Delve into the existence and stability of self-similar solutions for wave maps equations when the target manifold is a perturbed sphere. Learn about the known self-similar blowup solutions for spherical target manifolds and their asymptotic nonlinear stability against small perturbations. Discover how perturbative methods demonstrate the existence and asymptotic nonlinear stability of self-similar solutions for perturbed sphere target manifolds. This talk was presented as part of the Thematic Programme on "Nonlinear Waves and Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI).

Alexander Wittenstein - Existence and stability of corotational wave maps into perturbed spheres