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Strichartz Estimates on Schwarzschild Black Hole Backgrounds |
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| Authors: | Jeremy Marzuola Jason Metcalfe Daniel Tataru Mihai Tohaneanu |
| Affiliation: | 1. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA 2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599-3250, USA 3. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA 4. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA |
| 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 [29], 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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