On Global Existence of 3D Charge Critical Dirac-Klein-Gordon system

TL;DR

This paper establishes the global existence and well-posedness of the charge critical Dirac-Klein-Gordon system in three dimensions for small initial data, utilizing scale-invariant spaces with angular regularity.

Contribution

It is the first to prove global well-posedness for the critical 3D Dirac-Klein-Gordon system, extending results to large data via finite speed propagation.

Findings

Proved global well-posedness for small initial data in critical spaces.

Established local well-posedness for large initial data.

First result on the critical 3D Dirac-Klein-Gordon system.

Abstract

In this paper, we prove the global well-posedness property of charge critical Dirac-Klein-Gordon (DKG) system in $\mathbb{R}^{3+1}$ for small initial data in a space of scale invariant data which has extra weighted regularity in the angular variables. Therefore, by finite speed propagation, we could also derive the local well-posedness property for large initial data in the same space. To author's knowledge, our result appears to be the first result on the critical 3D DKG.