Global existence for coupled Klein-Gordon equations with different speeds

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2463-2506
Number of pages44
JournalAnnales de l'Institut Fourier
Volume61
Issue number6
DOIs
StatePublished - 2011

Fingerprint

Klein-Gordon Equation
Scatter
Global Solution
Global Existence
Space-time
Nonlinearity
Arbitrary

Keywords

  • Global existence
  • Klein-Gordon
  • Resonances

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Global existence for coupled Klein-Gordon equations with different speeds. / Germain, Pierre.

In: Annales de l'Institut Fourier, Vol. 61, No. 6, 2011, p. 2463-2506.

Research output: Contribution to journalArticle

@article{b777e61afc90409090d0fee9e6a1840c,
title = "Global existence for coupled Klein-Gordon equations with different speeds",
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.",
keywords = "Global existence, Klein-Gordon, Resonances",
author = "Pierre Germain",
year = "2011",
doi = "10.5802/aif.2680",
language = "English (US)",
volume = "61",
pages = "2463--2506",
journal = "Annales de l'Institut Fourier",
issn = "0373-0956",
publisher = "Association des Annales de l'Institut Fourier",
number = "6",

}

TY - JOUR

T1 - Global existence for coupled Klein-Gordon equations with different speeds

AU - Germain, Pierre

PY - 2011

Y1 - 2011

N2 - 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.

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.

KW - Global existence

KW - Klein-Gordon

KW - Resonances

UR - http://www.scopus.com/inward/record.url?scp=84860320260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860320260&partnerID=8YFLogxK

U2 - 10.5802/aif.2680

DO - 10.5802/aif.2680

M3 - Article

VL - 61

SP - 2463

EP - 2506

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 6

ER -