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We prove that the Cauchy problem for the Dirac-Klein-Gordon system ofequations in 1+3 dimensions is locally well-posed in a range of Sobolev spacesfor the Dirac spinor and the meson field. The result contains and extends theearlier known results for the same problem. Our proof relies on the nullstructure in the system, and bilinear spacetime estimates ofKlainerman-Machedon type.

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