Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 93, pp. 1-17.

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

Authors: Hailiang Li (Univ. of Vienna, Austria)
         Chi-Kun Lin (National Cheng Kung Univ., Taiwan)

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.
 
Submitted April 1, 2002. Published September 8, 2003.
Math Subject Classifications: 35A05, 35Q55.
Key Words: Schrodinger-Poisson system; quantum hydrodynamics;
           Euler-Poisson system; semiclassical limit; WKB expansion;
           quasilinear symmetric hyperbolic system.