Finite time blowup for the fourth-order NLS

Yonggeun Cho, Tohru Ozawa, Chengbo Wang

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We consider the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity (−|x|−2|u|4/n u) in high space dimensions. Extending Glassey’s virial argument, we show the finite time blowup of solutions when the energy is negative.

    Original languageEnglish
    Pages (from-to)615-640
    Number of pages26
    JournalBulletin of the Korean Mathematical Society
    Volume53
    Issue number2
    DOIs
    Publication statusPublished - 2016

    Fingerprint

    Finite Time Blow-up
    Fourth-order Equations
    Blow-up of Solutions
    Fourth Order
    Nonlinearity
    Energy

    Keywords

    • Finite time blowup
    • Fourth order NLS
    • Mass-critical
    • Virial argument

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Finite time blowup for the fourth-order NLS. / Cho, Yonggeun; Ozawa, Tohru; Wang, Chengbo.

    In: Bulletin of the Korean Mathematical Society, Vol. 53, No. 2, 2016, p. 615-640.

    Research output: Contribution to journalArticle

    Cho, Yonggeun ; Ozawa, Tohru ; Wang, Chengbo. / Finite time blowup for the fourth-order NLS. In: Bulletin of the Korean Mathematical Society. 2016 ; Vol. 53, No. 2. pp. 615-640.
    @article{89c24c79f49a4ef1b2187dcb3e8f311a,
    title = "Finite time blowup for the fourth-order NLS",
    abstract = "We consider the fourth-order Schr{\"o}dinger equation with focusing inhomogeneous nonlinearity (−|x|−2|u|4/n u) in high space dimensions. Extending Glassey’s virial argument, we show the finite time blowup of solutions when the energy is negative.",
    keywords = "Finite time blowup, Fourth order NLS, Mass-critical, Virial argument",
    author = "Yonggeun Cho and Tohru Ozawa and Chengbo Wang",
    year = "2016",
    doi = "10.4134/BKMS.2016.53.2.615",
    language = "English",
    volume = "53",
    pages = "615--640",
    journal = "Bulletin of the Korean Mathematical Society",
    issn = "1015-8634",
    publisher = "Korean Mathematical Society",
    number = "2",

    }

    TY - JOUR

    T1 - Finite time blowup for the fourth-order NLS

    AU - Cho, Yonggeun

    AU - Ozawa, Tohru

    AU - Wang, Chengbo

    PY - 2016

    Y1 - 2016

    N2 - We consider the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity (−|x|−2|u|4/n u) in high space dimensions. Extending Glassey’s virial argument, we show the finite time blowup of solutions when the energy is negative.

    AB - We consider the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity (−|x|−2|u|4/n u) in high space dimensions. Extending Glassey’s virial argument, we show the finite time blowup of solutions when the energy is negative.

    KW - Finite time blowup

    KW - Fourth order NLS

    KW - Mass-critical

    KW - Virial argument

    UR - http://www.scopus.com/inward/record.url?scp=84962040456&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84962040456&partnerID=8YFLogxK

    U2 - 10.4134/BKMS.2016.53.2.615

    DO - 10.4134/BKMS.2016.53.2.615

    M3 - Article

    AN - SCOPUS:84962040456

    VL - 53

    SP - 615

    EP - 640

    JO - Bulletin of the Korean Mathematical Society

    JF - Bulletin of the Korean Mathematical Society

    SN - 1015-8634

    IS - 2

    ER -