Asymptotic analysis of solutions to a gauged $\mathrm{O}\left(3\right)$ sigma model

Bartolucci, Daniele; Lee, Youngae; Lin, Chang-Shou; Onodera, Michiaki

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 651-685.

We analyze an elliptic equation arising in the study of the gauged $\mathrm{O}\left(3\right)$ 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 ${ℝ}^2$, 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.

Mots clés : Gauged $ \mathrm{O}(3)$ sigma models, Blow up analysis, Pohozaev type identity, Stable solutions

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