A note on energy currents and decay for the wave equation on a Schwarzschild background

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dc.creatorDafermos, Mihalis
dc.creatorRodnianski, Igor
dc.date2007-09-30
dc.date.accessioned2026-07-07T08:33:13Z
dc.date.available2026-07-07T08:33:13Z
dc.descriptionIn recent work, we have proven uniform decay bounds for solutions of the wave equation $\Box_gϕ=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|ϕ|\le Cv_+^{-1}$, which holds throughout the domain of outer communications, where $v$ is an advanced Eddington-Finkelstein coordinate, $v_+=\max\{v,1\}$, and $C$ is a constant depending on a Sobolev norm of initial data. A crucial estimate in the proof required a decomposition into spherical harmonics. We here give an alternative proof of this estimate not requiring such a decomposition.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0710.0171
dc.identifierhttp://arxiv.org/abs/0710.0171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139050
dc.subjectAnalysis of PDEs
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectDifferential Geometry
dc.titleA note on energy currents and decay for the wave equation on a Schwarzschild background
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