Electron. J. Diff. Eqns., Vol. 2007(2007), No. 162, pp. 1-26.

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

Achenef Tesfahun

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.

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Achenef Tesfahun
Department of Mathematical Sciences
Norwegian University of Science and Technology
Alfred Getz' vei 1, N-7491 Trondheim, Norway
email: tesfahun@math.ntnu.no

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