Blue, P.; Soffer, A. Semilinear wave equations on the Schwarzschild manifold. I: Local decay estimates. (English) Zbl 1044.58033 Adv. Differ. Equ. 8, No. 5, 595-614 (2003). The authors consider semi-linear wave equations on an outer Schwarzschild solution. After constructing a set of a-priori estimates, similar to the Morawetz estimate in flat space, local decay and other estimates are proved for the semi-linear wave equation on outer Schwarzschild solution in the \(L^2\)-sense. Radial symmetry for the initial conditions is not required and therefore the angular behaviour is not restricted. Reviewer: Thoralf Chrobok (Berlin) Cited in 51 Documents MSC: 58J45 Hyperbolic equations on manifolds 83C57 Black holes 35Q75 PDEs in connection with relativity and gravitational theory 35L05 Wave equation Keywords:outer Schwarzschild solution; semi-linear wave equation; Morawetz estimate PDFBibTeX XMLCite \textit{P. Blue} and \textit{A. Soffer}, Adv. Differ. Equ. 8, No. 5, 595--614 (2003; Zbl 1044.58033) Full Text: arXiv