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

Abstract

We show that global Strichartz estimates for magnetic Dirac operators generally fail, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, that is, with homogeneity-degree more than −1, such that the magnetic field points to a fixed direction, which does not depend on x ∈ R3 .