Geodesic
Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system
Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 877-899

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/100
Classification : 35-XX, 00-XX
Keywords: Dirac equation, Klein-Gordon equation, null structure, local well-posedness, null form estimates 
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     author = {Piero D'Ancona and Damiano Foschi and Sigmund Selberg},
     title = {Null structure and almost optimal local regularity for the {Dirac-Klein-Gordon} system},
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Piero D'Ancona; Damiano Foschi; Sigmund Selberg. Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system. Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 877-899. doi: 10.4171/jems/100

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