Space-time analytic smoothing effect for a system of nonlinear Schrödinger equations with non pseudo-conformally invariant interactions

Gaku Hoshino

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    In this study, we consider the local Cauchy problem for a system of nonlinear Schrödinger equations with non pseudo-conformally invariant interactions in the framework of space of charge and in the framework of space of energy. The main purpose of this study is to construct local solutions in function spaces of analytic vectors for the Galilei generator and the pseudo-conformal generator with data which satisfy exponentially decaying condition at spatial infinity. In particular, we improve the nonlinear estimates have been proved by Hayashi and Kato and Ozawa et al. involving the pseudo-conformal generator with coefficient which depends on time of local existence of solutions and has singularity at finite value.

    Original languageEnglish
    Pages (from-to)802-819
    Number of pages18
    JournalCommunications in Partial Differential Equations
    Volume42
    Issue number5
    DOIs
    Publication statusPublished - 2017 May 4

    Fingerprint

    Smoothing Effect
    System of Nonlinear Equations
    Nonlinear equations
    Space-time
    Generator
    Invariant
    Interaction
    Space of Analytic Functions
    Local Existence
    Local Solution
    Existence of Solutions
    Cauchy Problem
    Charge
    Infinity
    Singularity
    Energy
    Estimate
    Framework

    Keywords

    • Analytic smoothing effect
    • mass resonance
    • nonlinear Schrödinger equation

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    @article{145f6ca1fe8241f19f77166b2c47c79b,
    title = "Space-time analytic smoothing effect for a system of nonlinear Schr{\"o}dinger equations with non pseudo-conformally invariant interactions",
    abstract = "In this study, we consider the local Cauchy problem for a system of nonlinear Schr{\"o}dinger equations with non pseudo-conformally invariant interactions in the framework of space of charge and in the framework of space of energy. The main purpose of this study is to construct local solutions in function spaces of analytic vectors for the Galilei generator and the pseudo-conformal generator with data which satisfy exponentially decaying condition at spatial infinity. In particular, we improve the nonlinear estimates have been proved by Hayashi and Kato and Ozawa et al. involving the pseudo-conformal generator with coefficient which depends on time of local existence of solutions and has singularity at finite value.",
    keywords = "Analytic smoothing effect, mass resonance, nonlinear Schr{\"o}dinger equation",
    author = "Gaku Hoshino",
    year = "2017",
    month = "5",
    day = "4",
    doi = "10.1080/03605302.2017.1295063",
    language = "English",
    volume = "42",
    pages = "802--819",
    journal = "Communications in Partial Differential Equations",
    issn = "0360-5302",
    publisher = "Taylor and Francis Ltd.",
    number = "5",

    }

    TY - JOUR

    T1 - Space-time analytic smoothing effect for a system of nonlinear Schrödinger equations with non pseudo-conformally invariant interactions

    AU - Hoshino, Gaku

    PY - 2017/5/4

    Y1 - 2017/5/4

    N2 - In this study, we consider the local Cauchy problem for a system of nonlinear Schrödinger equations with non pseudo-conformally invariant interactions in the framework of space of charge and in the framework of space of energy. The main purpose of this study is to construct local solutions in function spaces of analytic vectors for the Galilei generator and the pseudo-conformal generator with data which satisfy exponentially decaying condition at spatial infinity. In particular, we improve the nonlinear estimates have been proved by Hayashi and Kato and Ozawa et al. involving the pseudo-conformal generator with coefficient which depends on time of local existence of solutions and has singularity at finite value.

    AB - In this study, we consider the local Cauchy problem for a system of nonlinear Schrödinger equations with non pseudo-conformally invariant interactions in the framework of space of charge and in the framework of space of energy. The main purpose of this study is to construct local solutions in function spaces of analytic vectors for the Galilei generator and the pseudo-conformal generator with data which satisfy exponentially decaying condition at spatial infinity. In particular, we improve the nonlinear estimates have been proved by Hayashi and Kato and Ozawa et al. involving the pseudo-conformal generator with coefficient which depends on time of local existence of solutions and has singularity at finite value.

    KW - Analytic smoothing effect

    KW - mass resonance

    KW - nonlinear Schrödinger equation

    UR - http://www.scopus.com/inward/record.url?scp=85018369032&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85018369032&partnerID=8YFLogxK

    U2 - 10.1080/03605302.2017.1295063

    DO - 10.1080/03605302.2017.1295063

    M3 - Article

    VL - 42

    SP - 802

    EP - 819

    JO - Communications in Partial Differential Equations

    JF - Communications in Partial Differential Equations

    SN - 0360-5302

    IS - 5

    ER -