An improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation

Tohru Ozawa, Nicola Visciglia

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    We revise the classical approach by Brézis-Gallouët to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in R2 with initial data in H2(Ω)∩H01(Ω), and for the quartic nonlinear half-wave equation on R with initial data in H1(R).

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    Global Well-posedness
    Wave equations
    Quartic
    Wave equation
    Nonlinear Evolution Equations

    Keywords

    • Energy estimates
    • Global existence
    • Half-wave equation
    • Nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Analysis
    • Mathematical Physics

    Cite this

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    title = "An improvement on the Br{\'e}zis-Gallou{\"e}t technique for 2D NLS and 1D half-wave equation",
    abstract = "We revise the classical approach by Br{\'e}zis-Gallou{\"e}t to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in R2 with initial data in H2(Ω)∩H01(Ω), and for the quartic nonlinear half-wave equation on R with initial data in H1(R).",
    keywords = "Energy estimates, Global existence, Half-wave equation, Nonlinear Schr{\"o}dinger equation",
    author = "Tohru Ozawa and Nicola Visciglia",
    year = "2014",
    month = "9",
    day = "12",
    doi = "10.1016/j.anihpc.2015.03.004",
    language = "English",
    journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",
    issn = "0294-1449",
    publisher = "Elsevier Masson SAS",

    }

    TY - JOUR

    T1 - An improvement on the Brézis-Gallouët technique for 2D NLS and 1D half-wave equation

    AU - Ozawa, Tohru

    AU - Visciglia, Nicola

    PY - 2014/9/12

    Y1 - 2014/9/12

    N2 - We revise the classical approach by Brézis-Gallouët to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in R2 with initial data in H2(Ω)∩H01(Ω), and for the quartic nonlinear half-wave equation on R with initial data in H1(R).

    AB - We revise the classical approach by Brézis-Gallouët to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in R2 with initial data in H2(Ω)∩H01(Ω), and for the quartic nonlinear half-wave equation on R with initial data in H1(R).

    KW - Energy estimates

    KW - Global existence

    KW - Half-wave equation

    KW - Nonlinear Schrödinger equation

    UR - http://www.scopus.com/inward/record.url?scp=84926633540&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84926633540&partnerID=8YFLogxK

    U2 - 10.1016/j.anihpc.2015.03.004

    DO - 10.1016/j.anihpc.2015.03.004

    M3 - Article

    AN - SCOPUS:84926633540

    JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

    JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

    SN - 0294-1449

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