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 - Dec 1 2011

    Fingerprint

Keywords

  • Global existence
  • Klein-Gordon
  • Resonances

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this