Existence and nonlinear stability of stationary states for the semi-relativistic Schrödinger-Poisson system

2012/09/15 by Salem, Walid Abou, Chen, Thomas, Vougalter, Vitali
#82C10 #82D10 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/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.

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