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.