On Global Existence of 3D Charge Critical 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.

The inappropriate radial assumption is removed and the result is improved