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

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

2008-04-27

arxiv.org/abs/0804.4301v1

Mathematics

Analysis of PDEs

53 pages, 2 figures

Scientific paper

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 $L^2$ 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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