In recent work, Grunrock and Pecher proved that the Dirac-Klein-Gordon system in 2d is globally well-posed in the charge class (data in L(2) for the spinor and in a suitable Sobolev space for the scalar field). Here we obtain the analogous result for the full Maxwell-Dirac system in 2d. Making use of the null structure of the system, found in earlier joint work with Damiano Foschi, we first prove local well-posedness in the charge class. To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis. For this we rely on the fact that MD is charge subcritical in two space dimensions, and make use of the null structure of the Maxwell part. (C) 2010 Elsevier Inc. All rights reserved.
Global well-posedness of the Maxwell-Dirac system in two space dimensions / D'Ancona, Piero Antonio; S., Selberg. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 260:8(2011), pp. 2300-2365. [10.1016/j.jfa.2010.12.010]
Global well-posedness of the Maxwell-Dirac system in two space dimensions
D'ANCONA, Piero Antonio;
2011
Abstract
In recent work, Grunrock and Pecher proved that the Dirac-Klein-Gordon system in 2d is globally well-posed in the charge class (data in L(2) for the spinor and in a suitable Sobolev space for the scalar field). Here we obtain the analogous result for the full Maxwell-Dirac system in 2d. Making use of the null structure of the system, found in earlier joint work with Damiano Foschi, we first prove local well-posedness in the charge class. To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis. For this we rely on the fact that MD is charge subcritical in two space dimensions, and make use of the null structure of the Maxwell part. (C) 2010 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
