Salem, Walid Abou; Chen, Thomas; Vougalter, Vitali

On the generalized semi-relativistic Schrödinger-Poisson system in $\mathbb{R}^n$

Doc. Math., J. DMV 18, 343-357 (2013)


Summary: The Cauchy problem for the semi-relativistic Schrödinger-Poisson system of equations is studied in $R^n, n \ge 1$, for a wide class of nonlocal interactions. Furthermore, the asymptotic behavior of the solution as the mass tends to infinity is rigorously discussed, and compared with solutions to the non-relativistic Schrödinger-Poisson system.

Mathematics Subject Classification

82D10, 82C10


Schrödinger-Poisson system, mean-field dynamics, long-range interaction, functional spaces, density matrices, Cauchy problem, global existence, infinite mass limit