Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 162, pp. 1-26.

Title: Low regularity and local well-posedness for the 1+3 dimensional
       Dirac-Klein-Gordon system

Author: Achenef Tesfahun (Norwegian Univ. of Science and Technology, Norway)

Abstract: 
 We prove that the Cauchy problem for the Dirac-Klein-Gordon system
 of equations in 1+3 dimensions is locally well-posed in a range of
 Sobolev spaces for the Dirac spinor and the meson field. The result
 contains and extends the earlier known results for the same problem.
 Our proof relies on the null structure in the system, and bilinear
 spacetime estimates of Klainerman-Machedon type.
  
Submitted June 22, 2007. Published November 21, 2007.
Math Subject Classifications: 35Q40, 35L70.
Key Words: Dirac equation; Klein-Gordon equation; low regular solutions;
           local well-posedness.