Local and global well-posedness for the Chern-Simons-Dirac system in one dimension

Abstract

We consider the Cauchy problem for the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+1}$ with initial data in $H^s$. Almost optimal local well-posedness is obtained. Moreover, we show that the solution is global in time, provided that initial data for the spinor component has finite charge, or $L^2$ norm.