Joint BCAM-UPV/EHU Analysis and PDE seminar: Scattering for nonlinear waves outside two strictly convex obstacles

Abstract
We will be interested in the long time asymptotic of the defocusing energy-critical nonlinear wave equation posed outside an obstacle. For the problem in the free space, it is known that the solutions behave linearly in large time: we say that they scatter. A natural question is therefore to try to understand under which geometrical conditions on the obstacle scattering occurs. I will explain why we expect scattering outside any non-trapping obstacle (for which all the rays of geometrical optics go to infinity), but that such a result seems out of reach for now; and I will present a result of scattering in a trapping geometry: the exterior of two strictly convex obstacles, for which there is one, unstable, trapped trajectory. Joint work with Camille Laurent.

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