Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    Research output: Contribution to journal › Article

    5 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.
    @article{1d8e4c789b104f9cbe7e9693731815a3,
    title = "Global well-posedness of critical nonlinear Schr{\"o}dinger equations below L2",
    abstract = "The global well-posedness on the Cauchy problem of nonlinear Schr{\"o}dinger 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.",
    keywords = "Angular regularity, Critical nonlinearity below L, Global well-posedness, Hartree equations, Weighted Strichartz estimate",
    author = "Yonggeun Cho and Gyeongha Hwang and Tohru Ozawa",
    year = "2013",
    month = "4",
    doi = "10.3934/dcds.2013.33.1389",
    language = "English",
    volume = "33",
    pages = "1389--1405",
    journal = "Discrete and Continuous Dynamical Systems- Series A",
    issn = "1078-0947",
    publisher = "Southwest Missouri State University",
    number = "4",

    }

    TY - JOUR

    T1 - Global well-posedness of critical nonlinear Schrödinger equations below L2

    AU - Cho, Yonggeun

    AU - Hwang, Gyeongha

    AU - Ozawa, Tohru

    PY - 2013/4

    Y1 - 2013/4

    N2 - 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.

    AB - 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.

    KW - Angular regularity

    KW - Critical nonlinearity below L

    KW - Global well-posedness

    KW - Hartree equations

    KW - Weighted Strichartz estimate

    UR - http://www.scopus.com/inward/record.url?scp=84872111706&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84872111706&partnerID=8YFLogxK

    U2 - 10.3934/dcds.2013.33.1389

    DO - 10.3934/dcds.2013.33.1389

    M3 - Article

    VL - 33

    SP - 1389

    EP - 1405

    JO - Discrete and Continuous Dynamical Systems- Series A

    JF - Discrete and Continuous Dynamical Systems- Series A

    SN - 1078-0947

    IS - 4

    ER -

    Access to Document