2006/08/15 by Pieter Blue, Avy Soffer, Blue, P. +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.gr-qc/0608073
openalex publication_date 2006/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.