Global energy solutions of Chern-Simons-Higgs equations in one space dimension

We study an initial value problem of Chern-Simons-Higgs equations in one space dimension. The global existence of solutions is proved for the finite energy data. Moreover, we study local well-posedness below the energy regularity, observing null forms of the system and applying bilinear estimates for wave-Sobolev space Hs,θ.