Virial identity and weak dispersion for the magnetic Dirac equation

TL;DR

This paper investigates the dispersive behavior of the magnetic Dirac equation, establishing virial identities, optimal smoothing and Strichartz estimates, and a Hardy inequality for the perturbed operator.

Contribution

It introduces a general virial identity and derives optimal dispersive estimates and a Hardy inequality for the magnetic Dirac system, advancing understanding of its mathematical properties.

Findings

Proved a general virial identity for the magnetic Dirac equation.

Established optimal smoothing and endpoint Strichartz estimates.

Derived a Hardy-type inequality for the perturbed Dirac operator.

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.