Strichartz estimates on Schwarzschild black hole backgrounds
arXiv:0802.3942 · doi:10.1007/s00220-009-0940-z
Abstract
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.
44 pages; typos fixed, minor modifications in several places