Local smoothing estimates for the massless Dirac-coulomb equation in 2 and 3 dimensions

Abstract

We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 space dimensions. Our strategy of proof is inspired by a paper of Burq et al. (2003) about Schroedinger and wave equations with inverse-square potentials, and relies on partial wave subspaces decomposition and spectral analysis of the Dirac-Coulomb operator.