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

    研究成果: Article

    抄録

    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.

    元の言語English
    ページ(範囲)2661-2678
    ページ数18
    ジャーナルDiscrete and Continuous Dynamical Systems- Series A
    39
    DOI
    出版物ステータスPublished - 2019 5 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

      ASJC Scopus subject areas

      • Analysis
      • Discrete Mathematics and Combinatorics
      • Applied Mathematics

      これを引用

      @article{214432bc5eb241faab028cdd408ab3f2,
      title = "Local well-posedness and blow-up for the half ginzburg-landau-kuramoto equation with rough coefficients and potential",
      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.",
      keywords = "Blow-up, Commutator estimate, Fractional Ginzburg-Landau equation",
      author = "Luigi Forcella and Kazumasa Fujiwara and Gueorguiev, {Vladimir Simeonov} and Tohru Ozawa",
      year = "2019",
      month = "5",
      day = "1",
      doi = "10.3934/dcds.2019111",
      language = "English",
      volume = "39",
      pages = "2661--2678",
      journal = "Discrete and Continuous Dynamical Systems- Series A",
      issn = "1078-0947",
      publisher = "Southwest Missouri State University",

      }

      TY - JOUR

      T1 - Local well-posedness and blow-up for the half ginzburg-landau-kuramoto equation with rough coefficients and potential

      AU - Forcella, Luigi

      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.

      KW - Blow-up

      KW - Commutator estimate

      KW - Fractional Ginzburg-Landau equation

      UR - http://www.scopus.com/inward/record.url?scp=85061305447&partnerID=8YFLogxK

      UR - http://www.scopus.com/inward/citedby.url?scp=85061305447&partnerID=8YFLogxK

      U2 - 10.3934/dcds.2019111

      DO - 10.3934/dcds.2019111

      M3 - Article

      VL - 39

      SP - 2661

      EP - 2678

      JO - Discrete and Continuous Dynamical Systems- Series A

      JF - Discrete and Continuous Dynamical Systems- Series A

      SN - 1078-0947

      ER -