On the focusing energy-critical fractional nonlinear schrödnger equations

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    研究成果: Article

    4 引用 (Scopus)

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    We consider the fractional nonlinear Schrödinger equation (FNLS) with non-local dispersion |∇|α and focusing energy-critical Hartree type nonlinearity [-(|x|-2α * |u|2)u]. We first establish a global well-posedness of radial case in energy space by adopting Kenig-Merle arguments [20] when the initial energy and initial kinetic energy are less than those of ground state, respectively. We revisit and highlight long time perturbation, profile decomposition and localized virial inequality. As an application of the localized virial inequality, we provide a proof for finite time blowup for energy critical Hartree equations via commutator technique introduced in [2].

    元の言語English
    ページ(範囲)161-192
    ページ数32
    ジャーナルAdvances in Differential Equations
    23
    発行部数3-4
    出版物ステータスPublished - 2018 3 1

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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