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

TL;DR

This paper investigates the behavior of solutions to the mass supercritical Chern-Simons-Schrödinger equations, establishing local well-posedness and analyzing conditions for scattering or blow-up in radial symmetry.

Contribution

It proves local well-posedness in radial spaces and characterizes the scattering versus blow-up dichotomy below the ground state threshold.

Findings

Established local well-posedness for radial solutions.

Identified conditions for scattering versus blow-up.

Analyzed solutions below the ground state threshold.

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.