On the well posedness of the magnetic Schrödinger-Poisson system in $R^3$

Jean-Marie Barbaroux (1, 2) , Vitali Vougalter (3)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332
3 Department of Mathematics [University of Toronto]

We prove global existence and uniqueness of strong solutions for the Schrödinger-Poisson system in the repulsive Coulomb case in R 3 in the presence of a smooth magnetic field.

Mots clés: functional spaces; density matrices; global existence and uniqueness; magnetic fields; Schrödinger-Poisson system

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Jean-Marie Barbaroux, Vitali Vougalter. On the well posedness of the magnetic Schrödinger-Poisson system in $R^3$. Mathematical Modelling of Natural Phenomena, 2017, 12 (1), pp.15 - 22. ⟨10.1051/mmnp/201712102⟩. ⟨hal-01465310⟩