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.
Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system / D'Ancona, Piero Antonio; D., Foschi; S., Selberg. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 9:(2007), pp. 877-899. [10.4171/JEMS/100]
Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system
D'ANCONA, Piero Antonio;
2007
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
