5 June 2013
The Einstein equation from general relativity is a quasilinear hyperbolic, geometric PDE (when viewed in an appropriate coordinate system) for a manifold. A particularly interesting set of known, exact solutions describe black holes. The wave and Maxwell equations on these manifolds are models for perturbations of the known solutions and have attracted a significant amount of attention in the last decade. Key estimates are conservation of energy and Morawetz (or integrated local energy) estimates. These can be proved using both Fourier analytic methods and more geometric methods. The main focus of the talk will be on decay estimates for solutions of the Maxwell equation outside a slowly rotating Kerr black hole.
- Partial Differential Equations Seminar