Title
Asymptotic stability of kinks for the Yang-Mills field
Abstract
In this talk I will present recent results on the asymptotic stability of stationary solutions (kinks) for nonlinear dispersive equations. I will begin with a brief overview of the field, then focus on a spherically symmetric and purely magnetic Yang-Mills field in an extremal Reissner-Nordstrom 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 dispersion in one dimension, 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 will explain how we extend and adapt viral 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. Time permitting, I will discuss open problems and ongoing research directions. This is joint work with C. Muñoz.
Please note that the seminar will take place in person in room 139 of Huxley Building.