Global existence of small solutions for quadratic quasilinear Klein–Gordon systems in two space dimensions

Consider a quasi-linear system of two Klein–Gordon equations with masses m 1, m 2. We prove that when m 1≠2 m 2 and m 2≠2 m 1, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308...

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Bibliographic Details
Published inJournal of functional analysis Vol. 211; no. 2; pp. 288 - 323
Main Authors Delort, Jean-Marc, Fang, Daoyuan, Xue, Ruying
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2004
Subjects
Global existence
Klainerman vector fields
Nonlinear Klein–Gordon equation
Klainerman vector fields
Global existence
Nonlinear Klein–Gordon equation
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Summary:Consider a quasi-linear system of two Klein–Gordon equations with masses m 1, m 2. We prove that when m 1≠2 m 2 and m 2≠2 m 1, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308) in the semi-linear case. Moreover, we show that global existence holds true also when m 1=2 m 2 and a convenient null condition is satisfied by the nonlinearities.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2004.01.008