Communications in Mathematical Physics

, Volume 282, Issue 3, pp 697–719

Decay and Non-Decay of the Local Energy for the Wave Equation on the De Sitter–Schwarzschild Metric

Article

DOI: 10.1007/s00220-008-0553-y

Cite this article as:
Bony, J. & Häfner, D. Commun. Math. Phys. (2008) 282: 697. doi:10.1007/s00220-008-0553-y

Abstract

We describe an expansion of the solution of the wave equation on the De Sitter–Schwarzschild metric in terms of resonances. The principal term in the expansion is due to a resonance at 0. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an \({\varepsilon}\) derivative loss in the angular directions.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux ITalence cedexFrance