Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates

A. Soffer; P. Blue

Semilinear wave equations on the Schwarzschild manifold I: Local decay estimates

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arxiv gr-qc/0310091 v2 pith:E35SBOKC submitted 2003-10-19 gr-qc

P. Blue , A. Soffer This is my paper · ORCID

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keywords estimatesdecaylocalmanifoldschwarzschildsemilinearwavea-priori

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The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.

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On turbulence for spacetimes with stable trapping
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On a fixed spacetime with stable trapping, the cubic wave equation produces a forward angular-mode cascade and growth of higher-order derivatives, behavior absent for linear waves.

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