Localized energy estimates for wave equations on high dimensional Schwarzschild space-times

Abstract

The localized energy estimate for the wave equation is known to be a fairly robust measure of dispersion. Recent analogs on the $(1+3)$-dimensional Schwarzschild space-time have played a key role in a number of subsequent results, including a proof of Price's law. In this article, we explore similar localized energy estimates for wave equations on $(1+n)$-dimensional hyperspherical Schwarzschild space-times.

15 pages. (updated References to the August 27, 2010 posting)

References in corpus (4)

• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• A note on energy currents and decay for the wave equation on a Schwarzschild background
• Errata for ``Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds'', ``Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates'', and ``The wave equation on the Schwarzschild metric II: Local Decay for the spin 2 Regge Wheeler equation''
• Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole