On the focusing energy-critical fractional nonlinear schrödnger equations

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    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].

    Original languageEnglish
    Pages (from-to)161-192
    Number of pages32
    JournalAdvances in Differential Equations
    Volume23
    Issue number3-4
    Publication statusPublished - 2018 Mar 1

    Fingerprint

    Electric commutators
    Nonlinear equations
    Kinetic energy
    Ground state
    Nonlinear Equations
    Fractional
    Decomposition
    Energy
    Hartree Equation
    Finite Time Blow-up
    Global Well-posedness
    Commutator
    Ground State
    Nonlinearity
    Perturbation
    Decompose

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    On the focusing energy-critical fractional nonlinear schrödnger equations. / Cho, Yonggeun; Hwang, Gyeongha; Ozawa, Tohru.

    In: Advances in Differential Equations, Vol. 23, No. 3-4, 01.03.2018, p. 161-192.

    Research output: Contribution to journalArticle

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