Local well-posedness of the Maxwell–Chern–Simons–Higgs system in the temporal gauge

In this paper, we investigate the local well-posedness of the Maxwell–Chern–Simons–Higgs system in the temporal gauge. By using the Xs,bXs,b type spaces, we prove that the system is locally well-posed in Hs×Hs−1(s≥1).