Existence and Nonlinear Stability of Stationary States for the Magnetic Schrödinger–Poisson System


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We study stationary states of the magnetic Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. We prove the existence and nonlinear stability for a wide class of stationary states by using the energy-Casimir method. We generalize the known global well-posedness result for the Schrödinger–Poisson system to the case where a magnetic field is involved.

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J.-M. Barbaroux

Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

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Email: barbarou@univ-tln.fr
法国, Campus de Luminy, Case 907, 163 Avenue de Luminy, Marseille cedex 9, 13288

V. Vougalter

University of Toronto

Email: barbarou@univ-tln.fr
加拿大, 27 King’s College Circle, Toronto, Ontario, M5S 1A1

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