A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

Soichiro Katayama; Tohru Ozawa; Hideaki Sunagawa

doi:10.1002/cpa.21392

A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

Soichiro Katayama^*, Tohru Ozawa, Hideaki Sunagawa

^*Corresponding author for this work

School of Advanced Science and Engineering

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

18 Citations (Scopus)

Abstract

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288-323), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition.

Original language	English
Pages (from-to)	1285-1302
Number of pages	18
Journal	Communications on Pure and Applied Mathematics
Volume	65
Issue number	9
DOIs	https://doi.org/10.1002/cpa.21392
Publication status	Published - 2012 Sept

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288-323), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition.",

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AB - We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288-323), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition.

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A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

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