DOCUMENTA MATHEMATICA, Vol. 18 (2013), 343-357

Walid Abou Salem, Thomas Chen, and Vitali Vougalter

On the Generalized Semi-Relativistic Schrödinger-Poisson System in R^n

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.

2010 Mathematics Subject Classification: 82D10, 82C10

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

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