Long-time existence for semilinear Klein–Gordon equations on compact manifolds for a generic mass

doi:https://doi.org/10.1016/j.crma.2015.06.012

Open AccessArticle10.1016/j.crma.2015.06.012

Long-time existence for semilinear Klein–Gordon equations on compact manifolds for a generic mass

Rafik Imekraz-2015-07-21-Comptes Rendus Mathématique

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TL;DRAbstract

The purpose of this note is to recap the results of long-time existence of small solutions for the semilinear Klein–Gordon equations on a boundaryless compact Riemannian manifold. Using a result by Zhang on the harmonic oscillator and Delort–Szeftel's estimates, we will explain how we can easily obtain a result that seems to be new: we improve the local existence time on compact manifolds whose eigenvalues are integers (like finite product of spheres).

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The purpose of this note is to recap the results of long-time existence of small solutions for the semilinear Klein–Gordon equations on a boundaryless compact Riemannian manifold. Using a result by Zhang on the harmonic oscillator and Delort–Szeftel's estimates, we will explain how we can easily obtain a result that seems to be new: we improve the local existence time on compact manifolds whose eigenvalues are integers (like finite product of spheres).

Keywords

MathematicsKlein–Gordon equationMathematical physicsManifold (fluid mechanics)Eigenvalues and eigenvectorsRiemannian manifoldPure mathematicsPhysics

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