Low regularity well-posedness for the one-dimensional Dirac - Klein - Gordon system
Abstract
Local well-posedness for the Dirac - Klein - Gordon equations is proven in one space dimension, where the Dirac part belongs to H-1/4+ε and the Klein - Gordon part to H1/4-ε for 0 < ε < 1/4, and global well-posedness, if the Dirac part belongs to the charge class L2 and the Klein - Gordon 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.
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