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''

Abstract

In ``Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds'' (math-ph/0002030), ``Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates'' (gr-qc/0310091), and ``The wave equation on the Schwarzschild metric II: Local Decay for the spin 2 Regge Wheeler equation'' (gr-qc/0310066), local decay estimates were proven for the (decoupled) Schrodinger, wave, and Regge-Wheeler equations on the Schwarzschild manifold, using commutator methods. Here, we correct a step in the commutator argument. The corrected argument works either for radial semilinear equations or general linear equations. This recovers the results in math-ph/0002030 and gr-qc/0310066, but does not recover the non radial, large data, semilinear result asserted in the gr-qc/0310091.

6 pages; Latex; v2: corrected typos and clarified exposition. v3: Acknowledgement

References in corpus (5)

• Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
• Decay of Solutions of the Wave Equation in the Kerr Geometry
• Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates
• Phase Space Analysis on some Black Hole Manifolds
• The wave equation on the Schwarzschild metric II: Local decay for the spin 2 Regge Wheeler equation

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• The wave equation on Schwarzschild-de Sitter spacetimes
• Phase Space Analysis on some Black Hole Manifolds
• Decay of solutions to the Maxwell equation on the Schwarzschild background
• The Strauss conjecture on asymptotically flat space-times
• Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior
• On the global stability of the wave-map equation in Kerr spaces with small angular momentum
• Localized energy estimates for wave equations on high dimensional Schwarzschild space-times
• A note on the wave equation on black hole spacetimes with small non-decaying first order terms
• Localized energy estimates on Myers-Perry space-times
• Global existence for a coupled wave system related to the Strauss conjecture