Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds |
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| Authors: | D Bambusi J‐M Delort B Grébert J Szeftel |
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| Institution: | 1. Università degli studi di Milano, Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy;2. Université Paris‐Nord;3. Université de Nantes, Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France;4. Princeton University, Fine Hall, Washington Road, Princeton NJ 08544‐1000;5. Université Bordeaux 1, Mathématiques Appliquées, UMR CNRS 5466, 351 cours de la Libération, 33405 Talence, France |
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| 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. © 2007 Wiley Periodicals, Inc. |
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