Global small solutions to the critical radial Dirac equation with potential

TL;DR

This paper proves the existence of global small solutions to a critical radial Dirac equation with a small potential, utilizing new endpoint estimates for the perturbed Dirac flow.

Contribution

It introduces novel endpoint estimates for the perturbed Dirac flow, enabling the analysis of global solutions with small critical norm data.

Findings

Established global existence of small solutions for the perturbed radial Dirac equation.

Developed new endpoint estimates for the perturbed Dirac flow.

Demonstrated the effectiveness of these estimates for radial-type initial data.

Abstract

We solve globally a radial cubic Dirac equation perturbed with a small potential, with data of small critical norm $H^{1}$. The main tool are new endpoint estimates of the perturbed Dirac flow for a class of radial-type initial data.