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. Journal of Differential Equations, 2012, 252 (10), pp.5613-5661. ⟨10.1016/j.jde.2012.01.031⟩. ⟨hal-00525251v2⟩