Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    Research output: Contribution to journal › Article

    6 Citations (Scopus)

    Abstract

    The global well-posedness on the Cauchy problem of nonlinear Schrödinger equations (NLS) is studied for a class of critical nonlinearity below L2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.

    Original languageEnglish
    Pages (from-to)1389-1405
    Number of pages17
    JournalDiscrete and Continuous Dynamical Systems- Series A
    Volume33
    Issue number4
    DOIs
    Publication statusPublished - 2013 Apr

    Fingerprint

    Global Well-posedness
    Nonlinear equations
    Nonlinear Equations
    Strichartz Estimates
    Weighted Estimates
    Polar coordinates
    Cauchy Problem
    Regularity
    Nonlinearity
    Term
    Estimate
    Class

    Keywords

    • Angular regularity
    • Critical nonlinearity below L
    • Global well-posedness
    • Hartree equations
    • Weighted Strichartz estimate

    ASJC Scopus subject areas

    • Discrete Mathematics and Combinatorics
    • Applied Mathematics
    • Analysis

    Cite this

    Global well-posedness of critical nonlinear Schrödinger equations below L2 . / Cho, Yonggeun; Hwang, Gyeongha; Ozawa, Tohru.

    In: Discrete and Continuous Dynamical Systems- Series A, Vol. 33, No. 4, 04.2013, p. 1389-1405.

    Research output: Contribution to journal › Article

    Cho, Y, Hwang, G & Ozawa, T 2013, 'Global well-posedness of critical nonlinear Schrödinger equations below L2 ', Discrete and Continuous Dynamical Systems- Series A, vol. 33, no. 4, pp. 1389-1405. https://doi.org/10.3934/dcds.2013.33.1389
    Cho Y, Hwang G, Ozawa T. Global well-posedness of critical nonlinear Schrödinger equations below L2 Discrete and Continuous Dynamical Systems- Series A. 2013 Apr;33(4):1389-1405. https://doi.org/10.3934/dcds.2013.33.1389
    Cho, Yonggeun ; Hwang, Gyeongha ; Ozawa, Tohru. / Global well-posedness of critical nonlinear Schrödinger equations below L2 In: Discrete and Continuous Dynamical Systems- Series A. 2013 ; Vol. 33, No. 4. pp. 1389-1405.
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