# Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain^{[1]}

- [1] Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, N.Y. 10012-1185 USA

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 6, page 2463-2506
- ISSN: 0373-0956

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topGermain, Pierre. "Global existence for coupled Klein-Gordon equations with different speeds." Annales de l’institut Fourier 61.6 (2011): 2463-2506. <http://eudml.org/doc/219797>.

@article{Germain2011,

abstract = {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.},

affiliation = {Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York, N.Y. 10012-1185 USA},

author = {Germain, Pierre},

journal = {Annales de l’institut Fourier},

keywords = {Klein-Gordon; global existence; resonances; two speeds of propagation; three space dimensions; separation of resonances},

language = {eng},

number = {6},

pages = {2463-2506},

publisher = {Association des Annales de l’institut Fourier},

title = {Global existence for coupled Klein-Gordon equations with different speeds},

url = {http://eudml.org/doc/219797},

volume = {61},

year = {2011},

}

TY - JOUR

AU - Germain, Pierre

TI - Global existence for coupled Klein-Gordon equations with different speeds

JO - Annales de l’institut Fourier

PY - 2011

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 6

SP - 2463

EP - 2506

AB - 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.

LA - eng

KW - Klein-Gordon; global existence; resonances; two speeds of propagation; three space dimensions; separation of resonances

UR - http://eudml.org/doc/219797

ER -

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