Electron. J. Diff. Eqns.,
Vol. 2007(2007), No. 162, pp. 126.
Low regularity and local wellposedness for the 1+3 dimensional
DiracKleinGordon system
Achenef Tesfahun
Abstract:
We prove that the Cauchy problem for the DiracKleinGordon system
of equations in 1+3 dimensions is locally wellposed 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 KlainermanMachedon type.
Submitted June 22, 2007. Published November 21, 2007.
Math Subject Classifications: 35Q40, 35L70.
Key Words: Dirac equation; KleinGordon equation; low regular solutions;
local wellposedness.
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Achenef Tesfahun
Department of Mathematical Sciences
Norwegian University of Science and Technology
Alfred Getz' vei 1, N7491 Trondheim, Norway
email: tesfahun@math.ntnu.no

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