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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    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Mathematical Physics

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