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 journalArticle

    12 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

    Fingerprint

    Null Condition
    Sobolev spaces
    Weighted Sobolev Spaces
    Global Existence
    Cauchy Problem
    Nonlinearity

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions. / Katayama, Soichiro; Ozawa, Tohru; Sunagawa, Hideaki.

    In: Communications on Pure and Applied Mathematics, Vol. 65, No. 9, 09.2012, p. 1285-1302.

    Research output: Contribution to journalArticle

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