LOW REGULARITY WELL-POSEDNESS FOR THE ONE-DIMENSIONAL DIRAC-KLEIN-GORDON SYSTEM

Local well-posedness for Dirac-Klein-Gordon equations is proven in one space dimension, where the Dirac part belongs to H-1/4+is an element of and the Klein-Gordon part to H1/4-is an element of for 0 < is an element of < 1/4, and global well-posedness, if the Dirac part belongs to the charge class L-2 and the Klein-Gordon part to II kappa with 0 < kappa < 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.