Kink Dynamics for the Yang-Mills Field in an Extremal Black Hole
Date:
Abstract
In this talk we present recent results on the asymptotic stability of kink solutions for nonlinear dispersive equations. I began with a brief overview of the field, then focus on the Yang-Mills model in an extremal Reissner-Nordström background. Here, the kink is a stationary solution that is strongly unstable and lacks an explicit form.
What makes this problem particularly challenging is the combination of weak 1D dispersion, an inverse-square decay of the linearized potential, and the presence of a weak threshold resonance, requiring new ideas and technicalities in the proof.
I explaint how we extend and adapt virial techniques in the spirit of Kowalczyk, Martel, and Muñoz to this setting, allowing us to prove asymptotic stability in the energy space and to construct an explicit finite-codimensional stable manifold around the kink.
This is joint work with C. Muñoz.