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''

摘要

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