Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

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    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

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    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

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