References & Citations
Mathematics > Analysis of PDEs
Title: Global well-posedness of the Maxwell-Dirac system in two space dimensions
(Submitted on 10 Apr 2010 (v1), last revised 9 Aug 2010 (this version, v3))
Abstract: In recent work, Gr\"unrock 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.
Submission history
From: Sigmund Selberg [view email][v1] Sat, 10 Apr 2010 14:41:36 GMT (39kb)
[v2] Wed, 14 Apr 2010 15:44:07 GMT (40kb)
[v3] Mon, 9 Aug 2010 13:44:02 GMT (44kb)
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