Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 150, pp. 1-13.
Title: Low regularity well-posedness for the one-dimensional
Dirac-Klein-Gordon system
Author: Hartmut Pecher (Bergische Univ. Wuppertal, Germany)
Abstract:
Local well-posedness for Dirac-Klein-Gordon equations is proven in one
space dimension, where the Dirac part belongs to
$H^{-\frac{1}{4}+\epsilon}$ and
the Klein-Gordon part to $H^{\frac{1}{4}-\epsilon}$ 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.
Submitted June 28, 2006. Published December 5, 2006.
Math Subject Classifications: 35Q40, 35L70.
Key Words: Dirac-Klein-Gordon system; well-posedness;
Fourier restriction norm method.