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 H s , θ .