GP Seminar: Weak turbulence on Schwarzschild-AdS

Abstract: In the presence of confinement, nonlinear dispersive equations can exhibit weakly turbulent dynamics through a gradual transfer of energy from low to high frequencies. In general relativity, this phenomenon plays a central role in the problem of the stability of asymptotically AdS black holes.

In this talk, I will present a proof of weak turbulence for a quasilinear cubic wave equation on the Schwarzschild–AdS exterior, viewed as a model for the Einstein vacuum equations. For an open and dense set of black hole mass parameters, we construct solutions arising from arbitrarily small initial data that exhibit unbounded growth of higher Sobolev norms. This is based on joint work with Georgios Moschidis (EPFL).

This is a talk in our Geometry and Topology Seminar Series.