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

Abstract

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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.

How to cite

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Germain, 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 -

References

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