Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

Jun Kato, Tohru Ozawa

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

    Original languageEnglish
    Pages (from-to)48-71
    Number of pages24
    JournalJournal des Mathematiques Pures et Appliquees
    Volume95
    Issue number1
    DOIs
    Publication statusPublished - 2011 Jan

    Fingerprint

    Strichartz Estimates
    Klein-Gordon Equation
    Non-relativistic Limit
    Nonlinear Klein-Gordon Equation
    Polar coordinates
    Global Solution
    Norm
    Estimate

    Keywords

    • Angular regularity
    • Endpoint estimate
    • Klein-Gordon equation
    • Strichartz estimate

    ASJC Scopus subject areas

    • Applied Mathematics
    • Mathematics(all)

    Cite this

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    abstract = "We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schr{\"o}dinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.",
    keywords = "Angular regularity, Endpoint estimate, Klein-Gordon equation, Strichartz estimate",
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    AU - Kato, Jun

    AU - Ozawa, Tohru

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    N2 - We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

    AB - We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrödinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown.

    KW - Angular regularity

    KW - Endpoint estimate

    KW - Klein-Gordon equation

    KW - Strichartz estimate

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