Local and global solutions to the O(3)-sigma model with the Maxwell and the Chern-Simons gauges in [formula omitted

Abstract

In this paper we study the well-posedness of the (1+1)-dimensional Maxwell-Chern-Simons gauged O(3)-sigma model with the Lorenz gauge condition. First, we provide the global well-posedness of a solution in a high regular space. We also prove the existence of a global solution with the finite total energy. Moreover, we consider local well-posedness below the energy regularity by exploiting null form and wave-Sobolev space.