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Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
Author(s) -
Bambusi D.,
Delort J.M.,
Grébert B.,
Szeftel J.
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20181
Subject(s) - cauchy distribution , mathematics , laplace operator , hamiltonian (control theory) , eigenvalues and eigenvectors , dimension (graph theory) , pure mathematics , mathematical analysis , physics , mathematical optimization , quantum mechanics
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. © 2007 Wiley Periodicals, Inc.