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Semilinear wave equations on the Schwarzschild manifold. I: Local decay estimates. (English) Zbl 1044.58033

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.

MSC:

58J45 Hyperbolic equations on manifolds
83C57 Black holes
35Q75 PDEs in connection with relativity and gravitational theory
35L05 Wave equation
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