Article

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

  • Jean-François BonyAffiliated withInstitut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux I Email author 
  • , Dietrich HäfnerAffiliated withInstitut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux I

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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.