The global existence in the Cauchy problem of the Maxwell–Chern–Simons–Higgs system

Abstract

In this article we prove the global existence of solution of the classical Maxwell–Chern–Simons–Higgs equations in (2+1)-dimensional Minkowski space–time in the Lorentz gauge. We also prove that the topological solution of the Maxwell–Chern–Simons–Higgs system converges to that of Maxwell–Higgs system as the Chern–Simons constant κ goes to zero, reproducing the classical result by Moncrief [J. Math. Phys. 21, 2291 (1980)] on the global existence of the Maxwell–Klein–Gordon system in (2+1)-dimension.