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.
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