Endpoint estimates and global existence for the nonlinear Dirac equation with potential

TL;DR

This paper establishes endpoint estimates with angular regularity for the wave and Dirac equations with small potentials, leading to global existence results for the cubic Dirac equation with small initial data in critical spaces.

Contribution

It introduces new endpoint estimates with angular regularity for perturbed wave and Dirac equations, enabling global existence proofs in critical energy spaces.

Findings

Proved endpoint estimates with angular regularity for wave and Dirac equations with small potentials.

Established global existence for the cubic Dirac equation with small initial data in $H^{1}$.

Achieved global existence results for small radial data in the critical energy space.

Abstract

We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for small initial $H^{1}$ data with additional angular regularity. This implies in particular global existence in the critical energy space $H^{1}$ for small radial data.