Hartmut Pecher
Published 2006-06-22, updated 2006-12-05Version 2
Local well-posedness for the Dirac - Klein - Gordon equations is proven in one space dimension, where the Dirac part belongs to H^{-{1/4}+\epsilon} and the Klein - Gordon part to H^{{1/4}-\epsilon} for 0 < \epsilon < 1/4, and global well-posedness, if the Dirac part belongs to the charge class L^2 and the Klein - Gordon part to H^k 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.
Comments: 14 pages. Final version to appear in Electronic Journal of Differential Equations
Low regularity well-posedness for the Yang-Mills system in 2D
Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension
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