Null structure and almost optimal local regularity for the Dirac-Klein-Gordon system

• Autores: Piero D'Ancona, Damiano Foschi, Sigmund Selberg
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 9, Nº 4, 2007, págs. 877-900
• Idioma: inglés
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• Resumen

  • 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.