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

TL;DR

This paper establishes Strichartz estimates with angular regularity for 2D and 3D massless Dirac-Coulomb equations, advancing understanding of their dispersive properties and enabling local well-posedness results for nonlinear variants.

Contribution

It extends previous analysis by proving new Strichartz estimates with angular regularity and applies these to establish local well-posedness for nonlinear Dirac-Coulomb equations.

Findings

Proved Strichartz estimates with angular regularity for 2D and 3D massless Dirac-Coulomb equations.

Established local well-posedness for nonlinear Dirac-Coulomb equations with Hartree-type nonlinearities.

Enhanced the analytical tools for dispersive PDEs involving Dirac-Coulomb systems.

Abstract

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.