JournalsaihpcVol. 32, No. 3pp. 651–685

Asymptotic analysis of solutions to a gauged sigma model

  • Daniele Bartolucci

    University of Rome “Tor Vergata”, Department of Mathematics, Via della Ricerca Scientifica n. 1, 00133 Rome, Italy

  • Youngae Lee

    Center for Advanced Study in Theoretical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan

  • Chang-Shou Lin

    Taida Institute for Mathematical Sciences, Center for Advanced Study in Theoretical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan

  • Michiaki Onodera

    Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
Asymptotic analysis of solutions to a gauged \( O\left(\right.3\left.\right) \) sigma model cover
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Abstract

We analyze an elliptic equation arising in the study of the gauged sigma model with the Chern–Simons term. In this paper, we study the asymptotic behavior of solutions and apply it to prove the uniqueness of stable solutions. However, one of the features of this nonlinear equation is the existence of stable nontopological solutions in , which implies the possibility that a stable solution which blows up at a vortex point exists. To exclude this kind of blow up behavior is one of the main difficulties which we have to overcome.

Cite this article

Daniele Bartolucci, Youngae Lee, Chang-Shou Lin, Michiaki Onodera, Asymptotic analysis of solutions to a gauged sigma model. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 3, pp. 651–685

DOI 10.1016/J.ANIHPC.2014.03.001