The wave equation on hyperbolic spaces

Jean-Philippe Anker (1) , Vittoria Pierfelice (1) , Maria Vallarino (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Polito - Politecnico di Torino = Polytechnic of Turin

In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well-posedness results for the nonlinear wave equation.

Mots clés: Hyperbolic space; semilinear wave equation; dispersive estimate; Strichartz estimate; local well-posedness

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Jean-Philippe Anker, Vittoria Pierfelice, Maria Vallarino. The wave equation on hyperbolic spaces. 2010. ⟨hal-00525251v1⟩