A remark on low regularity solutions of the Chern-Simons-Dirac system

TL;DR

This paper provides an alternative proof for the low regularity well-posedness of the Chern-Simons-Dirac system in Coulomb gauge, avoiding null structure and establishing unconditional uniqueness.

Contribution

It introduces a novel proof technique for low regularity solutions of the Chern-Simons-Dirac system that bypasses the need for null structure analysis.

Findings

Proves low regularity well-posedness without null structure

Establishes unconditional uniqueness for solutions

Provides a simplified proof approach

Abstract

An alternative proof of low regularity well-posedness for the Chern-Simons-Dirac system in Coulomb gauge is given which completely avoids the use of any null structure similarly to a recent result of Bournaveas-Candy-Machihara. An unconditional uniqueness result is also given.