English

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

Dynamical Systems 2007-05-23 v1 Analysis of PDEs

Abstract

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.

Keywords

Cite

@article{arxiv.math/0510292,
  title  = {Almost global existence for Hamiltonian semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds},
  author = {Dario Bambusi and Jean-Marc Delort and Benoit Grebert and Jeremie Szeftel},
  journal= {arXiv preprint arXiv:math/0510292},
  year   = {2007}
}