On the lack of dispersion for a class of magnetic Dirac flows

Details On the lack of dispersion for a class of magnetic Dirac flows On the lack of dispersion for a class of magnetic Dirac flows

2011-07-05

arxiv.org/abs/1107.0843v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at in?nity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic ?field points to a ?fixed direction, which does not depend on $x\in \mathbb{R}^3$.

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