Virial identity and weak dispersion for the magnetic Dirac equation

Abstract

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of view. We also prove a Hardy-type inequality for the perturbed Dirac operator.

13 pages, typos in the statement of theorem 1.3 and clarification of the proof in subsection 3.2