Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

Tohru Ozawa, K. Yamauchi

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.

    Original languageEnglish
    Pages (from-to)492-497
    Number of pages6
    JournalJournal of Mathematical Analysis and Applications
    Volume364
    Issue number2
    DOIs
    Publication statusPublished - 2010 Apr 15

    Fingerprint

    Smoothing Effect
    Invariance
    Nonlinear equations
    Global Solution
    Nonlinear Equations
    Cubic equation
    Exponential Decay
    Analytic Solution
    Global Existence
    Cauchy
    Cauchy Problem
    Regularity
    Infinity
    Scaling

    Keywords

    • Analytic smoothing effect
    • Global solutions
    • Nonlinear Schrödinger equations

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Analytic smoothing effect for global solutions to nonlinear Schrödinger equations. / Ozawa, Tohru; Yamauchi, K.

    In: Journal of Mathematical Analysis and Applications, Vol. 364, No. 2, 15.04.2010, p. 492-497.

    Research output: Contribution to journalArticle

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    abstract = "We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schr{\"o}dinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.",
    keywords = "Analytic smoothing effect, Global solutions, Nonlinear Schr{\"o}dinger equations",
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