Strichartz estimates on Schwarzschild black hole backgrounds

Understand

We study dispersive properties for the wave equation in the Schwarzschild space-time.

• The first result we obtain is a local energy estimate.
• This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates.
• A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.