Existence and nonlinear stability of stationary states for the magnetic Schrödinger-Poisson system
Résumé
The article is devoted to the studies of the stationary states of the magnetic Schrödinger-Poisson system in the repulsive (plasma physics) Coulomb case. Particularly, we prove the existence and the nonlinear stability of a wide class of stationary states by virtue of the energy-Casimir method. We generalize the global well-posedness result for the Schrödinger-Poisson system obtained by Brezzi and Markowich to the case when a magnetic field is turned on.