Electron. J. Diff. Eqns., Vol. 2006(2006), No. 150, pp. 1-13.

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

Hartmut Pecher

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 less than $\epsilon$ less than 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 less than $k$ less than 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.

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Hartmut Pecher
Fachbereich Mathematik und Naturwissenschaften
Bergische Universitat Wuppertal
Gaustr. 20, D-42097 Wuppertal, Germany
email: Hartmut.Pecher@math.uni-wuppertal.de

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