Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds

2000/02/09 by I. Laba, A. Soffer
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.MP #msc:35 #msc:83

paper · pdf

published as Helv. Phys. Acta,vol72,no. 4 (1999)274-294 · 21 pages

arxiv created 2000/02/09 · arxiv updated 2009/11/30

Abstract

We consider the NLS on Schwarzschild manifold.For radial solutions with sufficiently localized initial data,global existence,L^p estimates and asymptotic completeness of the wave operators is proved

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• 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''
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• Global existence and scattering for the inhomogeneous nonlinear Schrödinger equation
• Existence of global solutions to the derivative NLS equation with the inverse scattering transform method