Abstract

The massless Dirac equation with a Coulomb potential is interesting both from a physical and a mathematical point of view; it appears in some physical models, for instance the 2D equation is used to describe the dynamics of carbon atoms in a sheet of non-perfect graphene, and on the mathematical side the homogeneity of degree -1 of the potential seems to have a critical behavior, as |x| goes to infinity, since Strichartz estimates are known to hold for potentials that decay faster and there are examples of potentials decaying slower such that the corresponding flows do not disperse. In this talk I will present a recent result concerning Strichartz estimates for the solutions of the massless Dirac-Coulomb equation in 2 and 3 dimension with additional angular regularity. It extends the result on R3 of Cacciafesta-Séré-Zhang and provides completely new estimates on R2. As an application we will discuss a local well-posedness result for a nonlinear system.