Advanced Search
Article Contents
Article Contents

Global well-posedness of the Chern-Simons-Higgs equations with finite energy

Abstract Related Papers Cited by
  • We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global well-posedness for more regular data. Moreover, we prove local well-posedness even below the energy regularity, using the the null structure of the system in Lorenz gauge and bilinear space-time estimates for wave-Sobolev norms.
    Mathematics Subject Classification: Primary: 35L70, 35Q40.


    \begin{equation} \\ \end{equation}
  • [1]

    N. Bournaveas, Low regularity solutions of the relativistic Chern-Simons-Higgs theory in the Lorentz gauge, Electronic Journal of Differential Equations, (2009), 1-10.


    D. Chae and K. Choe, Global existence in the Cauchy problem of the relativistic Chern-Simons-Higgs theory, Nonlinearity, 15 (2002), 747-758.doi: 10.1088/0951-7715/15/3/314.


    P. D'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, in "Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena" Contemporary Mathematics, 526, Amer. Math. Soc., Providence, RI, (2010), 125-150.doi: 10.1090/conm/526/10379.


    J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, Commun. Math. Phys., 82 (1981), 1-28.


    J. Hong, Y. Kim and P. Y. Pac, Multivortex solutions of the abelian Chern-Simons-Higgs theory, Phys. Rev. Lett., 64 (1990), 2230-2233.doi: 10.1103/PhysRevLett.64.2230.


    H. Huh, Local and global solutions of the Chern-Simons-Higgs system, Journal of Functional Analysis, 242 (2007), 526-549.doi: 10.1016/j.jfa.2006.09.009.


    H. Huh, Towards the Chern-Simons-Higgs equation with finite energy, Discrete and Continuous Dynamical Systems, 30 (2011), 1145-1159.doi: 10.3934/dcds.2011.30.1145.


    R. Jackiw and E. J. Weinberg, Self-dual Chern-Simons vortices, Phys. Rev. Lett., 64 (1990), 2234-2237.doi: 10.1103/PhysRevLett.64.2234.


    S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J., 74 (1994), 19-44doi: 10.1215/S0012-7094-94-07402-4.


    S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Communications in Partial Differential Equations, 35 (2010), 1029-1057.doi: 10.1080/03605301003717100.


    J. Yuan, Local well-posedness of Chern-Simons-Higgs system in the Lorentz gauge, Journal of Mathematical Physics, 52 (2011), 103706.doi: 10.1063/1.3645365.

  • 加载中

Article Metrics

HTML views() PDF downloads(142) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint