Local well-posedness of Chern-Simons-Higgs system in the Lorentz gauge

In this paper, we investigate the local well-posedness of the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge. By exploiting the null structure in the nonlinear terms of the equations, we reprove the low regularity result by Bournaveas ["Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge," Electron. J. Differ. Equ. 2009(114), pp. 1-10]. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3645365]