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

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

2006-06-22

arxiv.org/abs/math/0606555v2

Mathematics

Analysis of PDEs

14 pages. Final version to appear in Electronic Journal of Differential Equations

Scientific paper

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.

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