Global existence for coupled Klein-Gordon equations with different speeds
Annales de l'Institut Fourier, Volume 61 (2011) no. 6, p. 2463-2506
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.
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.
DOI : https://doi.org/10.5802/aif.2680
Classification:  35L70,  47H60
Keywords: Klein-Gordon, global existence, resonances
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     pages = {2463-2506},
     doi = {10.5802/aif.2680},
     mrnumber = {2976318},
     zbl = {1255.35162},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_6_2463_0}
}
Germain, Pierre. Global existence for coupled Klein-Gordon equations with different speeds. Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2463-2506. doi : 10.5802/aif.2680. http://www.numdam.org/item/AIF_2011__61_6_2463_0/

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