Global existence for coupled Klein-Gordon equations with different speeds
[Solutions globales pour des équations de Klein-Gordon avec des vitesses différentes couplées]
Germain, Pierre
Annales de l'Institut Fourier, Tome 61 (2011), p. 2463-2506 / Harvested from Numdam
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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.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/aif.2680
Classification:  35L70,  47H60
Mots clés: Klein-Gordon, existence globale, résonances 
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     author = {Germain, Pierre},
     title = {Global existence for coupled Klein-Gordon equations with different speeds},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {2463-2506},
     doi = {10.5802/aif.2680},
     zbl = {1255.35162},
     mrnumber = {2976318},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2011__61_6_2463_0}
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Germain, Pierre. Global existence for coupled Klein-Gordon equations with different speeds. Annales de l'Institut Fourier, Tome 61 (2011) pp. 2463-2506. doi : 10.5802/aif.2680. http://gdmltest.u-ga.fr/item/AIF_2011__61_6_2463_0/

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