Strichartz estimates on Schwarzschild black hole backgrounds
Jeremy Marzuola, Jason Metcalfe, Daniel Tataru, Mihai Tohaneanu
TL;DR
This paper establishes global Strichartz estimates for wave equations on Schwarzschild black hole backgrounds, providing insights into dispersive properties and analyzing solutions near the photon sphere.
Contribution
It introduces new global-in-time Strichartz estimates for wave equations in Schwarzschild space-time, with detailed analysis near the trapping photon sphere region.
Findings
Proved local energy estimates for wave equations in Schwarzschild space-time
Established global Strichartz estimates for solutions
Analyzed behavior of solutions near the photon sphere
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.
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