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

Abstract

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, |�^κ|²→1, away from the vortices and the blow‐up rate of |ψ^κ_j|² at the vortex point p_j.