Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

Abstract

This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.

Keywords

• Schrodinger-Poisson system
• quantum hydrodynamics
• Euler-Poisson system
• semiclassical limit
• WKB expansion
• quasilinear symmetric hyperbolic system.