Jean-Marie Barbaroux, Vitali Vougalter
Existence and nonlinear stability of stationary states for the magnetic Schrodinger-Poisson system
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ABSTRACT.  The article is devoted to the studies of the stationary states of the magnetic Schrodinger-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 Schrodinger-Poisson system to the case when a magnetic field is turned on.