Generalized Strichartz estimates for the massive Dirac equation with critical potentials
Analysis of PDEs
2025-10-28 v1
Abstract
In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the Aharonov-Bohm magnetic potential and the Coulomb potential. The proof makes use of the relativistic Hankel transform introduced in previous works of Cacciafesta, S\'er\'e and Cacciafesta, Fanelli for the massless systems, and here adapted to the massive case: this allows for an explicit representation of the solutions, which reduces the analysis to the proof of suitable estimates on the generalized eigenfunctions of the operators. To the best of our knowledge, these are the first dispersive estimates for the massive Dirac equation with critical potentials.
Keywords
Cite
@article{arxiv.2510.23283,
title = {Generalized Strichartz estimates for the massive Dirac equation with critical potentials},
author = {Federico Cacciafesta and Elena Danesi and Eric Séré},
journal= {arXiv preprint arXiv:2510.23283},
year = {2025}
}