Local well-posedness and blow-up for the half ginzburg-landau-kuramoto equation with rough coefficients and potential

Luigi Forcella, Kazumasa Fujiwara, Vladimir Simeonov Gueorguiev, Tohru Ozawa

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.

    Original languageEnglish
    Pages (from-to)2661-2678
    Number of pages18
    JournalDiscrete and Continuous Dynamical Systems- Series A
    Volume39
    DOIs
    Publication statusPublished - 2019 May 1

    Fingerprint

    Electric commutators
    Local Well-posedness
    Initial value problems
    Ginzburg-Landau
    Elliptic Operator
    Blow-up
    Rough
    Commutator Estimate
    Essential Self-adjointness
    Perturbation
    Blow-up of Solutions
    Coefficient
    Initial Value Problem
    Nonlinearity
    Metric

    Keywords

    • Blow-up
    • Commutator estimate
    • Fractional Ginzburg-Landau equation

    ASJC Scopus subject areas

    • Analysis
    • Discrete Mathematics and Combinatorics
    • Applied Mathematics

    Cite this

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    abstract = "We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.",
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    author = "Luigi Forcella and Kazumasa Fujiwara and Gueorguiev, {Vladimir Simeonov} and Tohru Ozawa",
    year = "2019",
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    AU - Fujiwara, Kazumasa

    AU - Gueorguiev, Vladimir Simeonov

    AU - Ozawa, Tohru

    PY - 2019/5/1

    Y1 - 2019/5/1

    N2 - We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.

    AB - We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.

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    KW - Fractional Ginzburg-Landau equation

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