%0 Journal Article
%T Uniqueness of topological multi-vortex solutions for a skew-symmetric Chern-Simons system
%A Hsin-Yuan Huang
%A Youngae Lee
%A Chang-Shou Lin
%J Mathematics
%D 2014
%I arXiv
%R 10.1063/1.4916290
%X Consider the following skew-symmetric Chern-Simons system \begin{equation*}\left \{ \begin{split} &\Delta u_{1}+\frac{1}{\varepsilon^2} e^{u_{2}}(1-e^{u_{1}})=4\pi \sum^{N_1}_{j=1}\delta_{p_{j,1}}\\ &\Delta u_{2}+\frac{1}{\varepsilon^2} e^{u_{1}}(1-e^{u_{2}})=4\pi \sum^{N_2}_{j=1}\delta_{p_{j,2}} \end{split}\right.\quad\text{ in }\quad\Omega, \end{equation*} where $\Omega$ is a flat 2-dimensional torus $\mathbb{T}^2$ or $\mathbb{R}^2$, $\varepsilon> 0$ is a coupling parameter, and $\delta_p$ denotes the Dirac measure concentrated at $p$. In this paper, we prove that, when the coupling parameter $\varepsilon$ is small, the topological type solutions to the above system are uniquely determined by the location of their vortex points. This result follows by the bubbling analysis and the non-degency of linearized equations.
%U http://arxiv.org/abs/1408.6574v1