Vitali Vougalter,
University of Cape Town
Title: Existence and nonlinear stability of stationary states for the semi-relativistic Schroedinger-Poisson system
We study the stationary states of the semi-relativistic Schroedinger-Poisson system in the repulsive (plasma physics) Coulomb case. In particular, we establish the existence and the nonlinear stability of a wide class of stationary states by means of the energy-Casimir method. We generalize our global well-posedness result for the semi-relativistic Schroedinger-Poisson system to spaces with higher regularity