Strichartz estimates for the 2D and 3D massless Dirac-Coulomb equations and applications

In this paper we continue the analysis of the dispersive properties of the 2D and 3D massless Dirac-Coulomb equations that has been started in arXiv:1503.00945 and arXiv:2101.07185. We prove a priori estimates of the solution of the mentioned systems, in particular Strichartz estimates with an additional angular regularity, exploiting the tools developed in the previous works. As an application, we show local well-posedness results for a Dirac-Coulomb equation perturbed with Hartree-type nonlinearities.
Comment: 28 pages, 3 figures