Global well-posedness in energy space for the Chern-Simons-Higgs system in temporal gauge

The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is globally well-posed in energy space improving a result of Huh. The proof uses the bilinear space-time estimates in wave-Sobolev spaces by d’Ancona, Foschi and Selberg, an $L_x^6{L}_t^2$-estimate for solutions of the wave equation, and also takes advantage of a null condition.