Remarks on some dispersive estimates

Yonggeun Cho, Tohru Ozawa, Suxia Xia

    Research output: Contribution to journalArticle

    35 Citations (Scopus)

    Abstract

    In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

    Original languageEnglish
    Pages (from-to)1121-1128
    Number of pages8
    JournalCommunications on Pure and Applied Analysis
    Volume10
    Issue number4
    DOIs
    Publication statusPublished - 2011 Jul

    Fingerprint

    Dispersive Estimates
    Bessel functions
    Initial value problems
    Strichartz Estimates
    Oscillatory Integrals
    Decay Estimates
    Bessel Functions
    Growth Conditions
    Initial Value Problem
    Smoothness
    Simplify
    Generalization

    Keywords

    • Bessel functions
    • Dispersive equations
    • Dispersive estimate
    • Oscillatory integral
    • Strichartz estimate
    • Time decay

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Remarks on some dispersive estimates. / Cho, Yonggeun; Ozawa, Tohru; Xia, Suxia.

    In: Communications on Pure and Applied Analysis, Vol. 10, No. 4, 07.2011, p. 1121-1128.

    Research output: Contribution to journalArticle

    Cho, Yonggeun ; Ozawa, Tohru ; Xia, Suxia. / Remarks on some dispersive estimates. In: Communications on Pure and Applied Analysis. 2011 ; Vol. 10, No. 4. pp. 1121-1128.
    @article{016404da3af940cbb511d69d011ad156,
    title = "Remarks on some dispersive estimates",
    abstract = "In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].",
    keywords = "Bessel functions, Dispersive equations, Dispersive estimate, Oscillatory integral, Strichartz estimate, Time decay",
    author = "Yonggeun Cho and Tohru Ozawa and Suxia Xia",
    year = "2011",
    month = "7",
    doi = "10.3934/cpaa.2011.10.1121",
    language = "English",
    volume = "10",
    pages = "1121--1128",
    journal = "Communications on Pure and Applied Analysis",
    issn = "1534-0392",
    publisher = "American Institute of Mathematical Sciences",
    number = "4",

    }

    TY - JOUR

    T1 - Remarks on some dispersive estimates

    AU - Cho, Yonggeun

    AU - Ozawa, Tohru

    AU - Xia, Suxia

    PY - 2011/7

    Y1 - 2011/7

    N2 - In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

    AB - In this paper we consider the initial value problem for i∂tu + ω(|r|)u = 0. Under suitable smoothness and growth conditions on ω, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

    KW - Bessel functions

    KW - Dispersive equations

    KW - Dispersive estimate

    KW - Oscillatory integral

    KW - Strichartz estimate

    KW - Time decay

    UR - http://www.scopus.com/inward/record.url?scp=82155191489&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=82155191489&partnerID=8YFLogxK

    U2 - 10.3934/cpaa.2011.10.1121

    DO - 10.3934/cpaa.2011.10.1121

    M3 - Article

    AN - SCOPUS:82155191489

    VL - 10

    SP - 1121

    EP - 1128

    JO - Communications on Pure and Applied Analysis

    JF - Communications on Pure and Applied Analysis

    SN - 1534-0392

    IS - 4

    ER -