Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system

Abstract

Local well-posedness for Dirac-Klein-Gordon equations is proven in one space dimension, where the Dirac part belongs to H-1/4+ɛ and the Klein-Gordon part to H1/4-ɛ for 0 < ɛ < 1/4, and global well-posedness, if the Dirac part belongs to the charge class L2 and the Klein-Glordon part to Hk with 0 < k < 1/2. The proof uses a null structure in both nonlinearities detected by d'Ancona, Foschi and Selberg and bilinear estimates in spaces of Bourgain-Klainerman-Machedon type.