Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system

Piero D'Ancona; Damiano Foschi; Sigmund Selberg

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Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system

Piero D'Ancona·Damiano Foschi·Sigmund Selberg

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Abstract

We prove almost optimal local well-posedness for the coupled Dirac-Klein-Gordon (DKG) system of equations in 1+3 dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman-Machedon type. It has been known for some time that the Klein-Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.

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Piero D'Ancona, Damiano Foschi, Sigmund Selberg. 2005-09-23. Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system. https://arxiv.org/abs/math/0509545

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