Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds

Dario Bambusi (1) , Jean-Marc Delort (2) , Benoît Grébert (3) , Jeremie Szeftel (4)

1 Dipartimento de Matematica [Milano]
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 LMJL - Laboratoire de Mathématiques Jean Leray
4 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux

This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on Zoll manifolds (e.g. spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on Zoll manifolds.

Mots clés: Almost global solutions; Klein-Gordon equation; Zoll manifold

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]

Dario Bambusi, Jean-Marc Delort, Benoît Grébert, Jeremie Szeftel. Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds. Communications on Pure and Applied Mathematics, 2007, 60 (11), pp.1665--1690. ⟨hal-00011236⟩