Normal form for semi-linear Klein–Gordon equations with superquadratic oscillators

We prove a long time existence result for semi-linear Klein–Gordon equations with a superquadratic potential for small and smooth initial datum. The proof relies on a weak separation of eigenvalues and specific multilinear estimates of eigenfunctions of superquadratic oscillators.

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 179; no. 4; pp. 535 - 575
Main Author Imekraz, Rafik
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.04.2016
Springer Verlag
Subjects
Analysis of PDEs
Mathematics
Mathematics and Statistics
37K45
Nonlinear
35B35
35B34
Normal form
Klein–Gordon
35Q55
Compact manifold
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Summary:We prove a long time existence result for semi-linear Klein–Gordon equations with a superquadratic potential for small and smooth initial datum. The proof relies on a weak separation of eigenvalues and specific multilinear estimates of eigenfunctions of superquadratic oscillators.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-015-0739-2