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Wave and Klein–Gordon
equations on hyperbolic spaces
Jean-Philippe Anker and Vittoria Pierfelice |
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Vol. 7 (2014), No. 4, 953–995
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Abstract |
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We consider the Klein–Gordon equation associated with the Laplace–Beltrami operator on real hyperbolic spaces of dimension ; as 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. |
Keywords
hyperbolic space, wave kernel, semilinear wave equation,
semilinear Klein–Gordon equation, dispersive estimate,
Strichartz estimate, global well-posedness
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Mathematical Subject Classification 2010
Primary: 35L05, 43A85, 43A90, 47J35
Secondary: 22E30, 35L71, 58D25, 58J45, 81Q05
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Milestones
Received: 3 August 2013
Accepted: 1 March 2014
Published: 27 August 2014
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Authors |
| Jean-Philippe Anker | |
| Fédération Denis Poisson (FR 2964)
& Laboratoire MAPMO (UMR 7349), Bâtiment de
Mathématiques Université d’Orléans & CNRS B.P. 6759 45067 Orléans cedex 2 France |
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| Vittoria Pierfelice | |
| Fédération Denis Poisson (FR 2964)
& Laboratoire MAPMO (UMR 7349), Bâtiment de
Mathématiques Université d’Orléans & CNRS B.P. 6759 45067 Orléans Cedex 2 France |
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