Low regularity solutions for Chern-Simons-Dirac systems in the temporal and Coulomb gauge

TL;DR

This paper establishes low regularity local well-posedness and unconditional uniqueness results for the Chern-Simons-Dirac system in both temporal and Coulomb gauges using Bourgain-Klainerman-Machedon spaces.

Contribution

It provides new low regularity well-posedness results and unconditional uniqueness for the Chern-Simons-Dirac system in two different gauges.

Findings

Proves local well-posedness in Bourgain-Klainerman-Machedon spaces.

Achieves unconditional uniqueness under stronger data assumptions.

Extends results to both temporal and Coulomb gauges.

Abstract

We prove low regularity local well-posedness results in Bourgain-Klainerman-Machedon spaces for the Chern-Simons-Dirac system in the temporal gauge and the Coulomb gauge. Under slightly stronger assumptions on the data we also obtain "unconditional" uniqueness in the natural solution spaces.