[Stabilité en grands temps pour des équations semi-linéaires de Klein–Gordon sur des variétés compactes avec une masse générique]
L'objet de cette note est de résumer les résultats de stabilité en temps grand pour les petites solutions de l'équation semi-linéaire de Klein–Gordon sur une variété riemannienne compacte sans bord. Nous expliquerons aussi comment obtenir facilement un résultat qui semble nouveau en utilisant un résultat de Zhang sur l'oscillateur harmonique et des estimées de Delort et Szeftel : nous améliorons le temps d'existence sur des variétés compactes dont les valeurs propres sont des entiers (comme des produits finis de sphères).
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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@article{CRMATH_2015__353_9_831_0,
author = {Imekraz, Rafik},
title = {Long-time existence for semilinear {Klein{\textendash}Gordon} equations on compact manifolds for a generic mass},
journal = {Comptes Rendus. Math\'ematique},
pages = {831--835},
publisher = {Elsevier},
volume = {353},
number = {9},
year = {2015},
doi = {10.1016/j.crma.2015.06.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.012/}
}
TY - JOUR AU - Imekraz, Rafik TI - Long-time existence for semilinear Klein–Gordon equations on compact manifolds for a generic mass JO - Comptes Rendus. Mathématique PY - 2015 SP - 831 EP - 835 VL - 353 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.06.012/ DO - 10.1016/j.crma.2015.06.012 LA - en ID - CRMATH_2015__353_9_831_0 ER -
%0 Journal Article %A Imekraz, Rafik %T Long-time existence for semilinear Klein–Gordon equations on compact manifolds for a generic mass %J Comptes Rendus. Mathématique %D 2015 %P 831-835 %V 353 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.06.012/ %R 10.1016/j.crma.2015.06.012 %G en %F CRMATH_2015__353_9_831_0
Imekraz, Rafik. Long-time existence for semilinear Klein–Gordon equations on compact manifolds for a generic mass. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 831-835. doi : 10.1016/j.crma.2015.06.012. http://www.numdam.org/articles/10.1016/j.crma.2015.06.012/
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