Asymptotics of Maxwell–Chern–Simons vortices on the unit disc

In this paper we are concerned with the asymptotic behavior of the relativistic Maxwell–Chern–Simons (MCS) vortices on the unit disc. We establish the existence of a radial solution of the static MCS equations which is a minimizer of the MCS functional in the class of radial functions, and derive the asymptotic limit of the radial solution. As a consequence, we obtain a set of elliptic linear equations which is a generalization of the London equation for the Ginzburg–Landau model.