Wave and Klein-Gordon equations on hyperbolic spaces
Résumé
We consider the Klein-Gordon equation associated with the Laplace-Beltrami operator Δ on real hyperbolic spaces of dimension n≥2; as Δ has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well-posedness results for the corresponding semilinear equation with low regularity data.
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