Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain

doi:10.5802/aif.2680

Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	2463-2506
Number of pages	44
Journal	Annales de l'Institut Fourier
Volume	61
Issue number	6
DOIs	https://doi.org/10.5802/aif.2680
State	Published - 2011

Keywords

Global existence
Klein-Gordon
Resonances

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.2680

Cite this

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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.

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KW - Resonances

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Global existence for coupled Klein-Gordon equations with different speeds

Abstract

Keywords

ASJC Scopus subject areas

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