Asymptotics for the vortex condensate solutions in Chern-Simons-Higgs theory

In this paper we study asymptotic behaviors of the maximal vortex condensate solutions in the Chern-Simons-Higgs theory when the coupling parameter κ goes to zero. Using Tarantello's weak convergence result for F₁₂ [16], we derive the weak convergence of A₀/κ. As a consequence we compute the locally uniform convergence rate of Higgs fields, |φ^κ|² → 1, away from the vortices and the blow-up rate of |ψ^κ_j|² at the vortex point p_j.