On stable self-similar blowup for corotational wave maps and equivariant Yang-Mills connections

Abstract

We consider corotational wave maps from Minkowski spacetime into the sphere and the equivariant Yang-Mills equation for all energy-supercritical dimensions. Both models have explicit self-similar finite time blowup solutions, which continue to exist even past the singularity. We prove the nonlinear asymptotic stability of these solutions in spacetime regions that approach the future light cone of the singularity. For this, we develop a general functional analytic framework in adapted similarity coordinates that allows to evolve the stable wave flow near a self-similar blowup solution in such spacetime regions.