DELORT, Jean-Marc; IMEKRAZ, Rafik

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DELORT, Jean-Marc
Laboratoire Analyse, Géométrie et Applications [LAGA]

IMEKRAZ, Rafik
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Communications in Partial Differential Equations. 2017, vol. 42, n° 3, p. 388-416

Taylor & Francis

Résumé en anglais

We investigate the long time existence of small and smooth solutions for the semi-linear Klein-Gordon equation on a compact boundaryless Riemannian manifold.Without any spectral or geometric assumption, our first result improves the lifespan obtained by the local theory.The previous result is proved under a generic condition of the mass.As a byproduct of the method, we examine the particular case where the manifold is a multidimensional torus and we give explicit examples of algebraic masses for which we can improve the local existence time.The analytic part of the proof relies on multilinear estimates of eigenfunctions and estimates of small divisors proved by Delort and Szeftel.The algebraic part of the proof relies on a multilinear version of the Roth theorem proved by Schmidt.< Réduire

Mots clés en anglais

Klein-Gordon

compact manifold

normal form

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194052

Project ANR

Analyse asymptotique des Equations aux dérivées partielles d'évolution - ANR-13-BS01-0010

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251