Existence and nonlinear stability of stationary states for the semi-relativistic Schrödinger-Poisson system
arXiv:1209.3446
Abstract
We study the stationary states of the semi-relativistic Schrödinger-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 the global well-posedness result of our previous work for the semi-relativistic Schrödinger-Poisson system to spaces with higher regularity.
Latex, 25 pages