Null structure and almost optimal local well-posedness of the Maxwell-Dirac system

2008/04/27 by D'Ancona, Piero, Foschi, Damiano, Selberg, Sigmund · 1 citation
#35L70 #35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0804.4301

Abstract

We uncover the full null structure of the Maxwell-Dirac system in Lorenz gauge. This structure, which cannot be seen in the individual component equations, but only when considering the system as a whole, is expressed in terms of tri- and quadrilinear integral forms with cancellations measured by the angles between spatial frequencies. In the 3D case, we prove frequency-localized L² space-time estimates for these integral forms at the scale invariant regularity up to a logarithmic loss, hence we obtain almost optimal local well-posedness of the system by iteration.

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• Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations

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