Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

Details Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

2007-06-04

arxiv.org/abs/0706.0350v1

Mathematics

Analysis of PDEs

22 pages, 5 figures

Scientific paper

We describe an expansion of the solution of the wave equation in the De
Sitter - Schwarzschild metric in terms of resonances. The main term in the
expansion is due to a zero resonance. The error term decays polynomially if we
permit a logarithmic derivative loss in the angular directions and
exponentially if we permit an small derivative loss in the angular directions.

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