Strichartz estimates on Schwarzschild black hole backgrounds

Details Strichartz estimates on Schwarzschild black hole backgrounds Strichartz estimates on Schwarzschild black hole backgrounds

2008-02-27

arxiv.org/abs/0802.3942v3

Mathematics

Analysis of PDEs

44 pages; typos fixed, minor modifications in several places

Scientific paper

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.

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