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.
Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds / D. Bambusi, J.M. Delort, B. Grébert, J. Szeftel. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 60:11(2007), pp. 1665-1690.
Almost global existence for Hamiltonian semilinear Klein-Gordon equations with small Cauchy data on Zoll manifolds
D. BambusiPrimo
;
2007
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.
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