Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system
Analysis of PDEs
2016-09-07 v1
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.
Keywords
Cite
@article{arxiv.math/0509545,
title = {Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system},
author = {Piero D'Ancona and Damiano Foschi and Sigmund Selberg},
journal= {arXiv preprint arXiv:math/0509545},
year = {2016}
}
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19 pages