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

Soichiro Katayama, Tohru Ozawa, Hideaki Sunagawa

Research output: Contribution to journalArticlepeer-review

14 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 languageEnglish
Pages (from-to)1285-1302
Number of pages18
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number9
DOIs
Publication statusPublished - 2012 Sep 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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