Scattering and blow-up for Chern-Simons-Schr\"odinger equations in the mass supercritical cas

Abstract

In this paper, we are concerned with solutions to the Cauchy problem for Chern-Simons-Schr\"odinger equations in the mass supercritical case. First we establish the local well-posedness of solutions in the radial space. Then we consider scattering versus blow-up dichotomy for radial data below the ground state threshold.