[Solutions globales pour des équations de Klein-Gordon avec des vitesses différentes couplées]
Soit, en dimension 3, un système d’équations de Klein-Gordon dont les vitesses sont différentes, avec des termes non-linéaires quadratiques. On montre, pour des données suffisamment petites, regulières et localisées, qu’une solution globale existe et qu’elle disperse. La preuve repose sur la méthode des résonances en espace-temps. La structure des résonances du système se trouve être d’un type qui n’avait pas été étudié jusqu’ici, mais qui est générique dans un certain sens.
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.
Keywords: Klein-Gordon, global existence, resonances
Mot clés : Klein-Gordon, existence globale, résonances
@article{AIF_2011__61_6_2463_0,
author = {Germain, Pierre},
title = {Global existence for coupled {Klein-Gordon} equations with different speeds},
journal = {Annales de l'Institut Fourier},
pages = {2463--2506},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {61},
number = {6},
year = {2011},
doi = {10.5802/aif.2680},
zbl = {1255.35162},
mrnumber = {2976318},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2680/}
}
TY - JOUR AU - Germain, Pierre TI - Global existence for coupled Klein-Gordon equations with different speeds JO - Annales de l'Institut Fourier PY - 2011 SP - 2463 EP - 2506 VL - 61 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2680/ DO - 10.5802/aif.2680 LA - en ID - AIF_2011__61_6_2463_0 ER -
%0 Journal Article %A Germain, Pierre %T Global existence for coupled Klein-Gordon equations with different speeds %J Annales de l'Institut Fourier %D 2011 %P 2463-2506 %V 61 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2680/ %R 10.5802/aif.2680 %G en %F AIF_2011__61_6_2463_0
Germain, Pierre. Global existence for coupled Klein-Gordon equations with different speeds. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2463-2506. doi : 10.5802/aif.2680. http://www.numdam.org/articles/10.5802/aif.2680/
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