Hailiang Li & Chi-Kun Lin
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.
An addendum was attached on August 17, 2006.
The authors made the following two corrections:
On the sixth line of Theorem 2.1, the expression should be replaced by .
On the fourteenth line of Theorem 2.2, the expression should be replaced by .
See last page of this manuscript for details.
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| Hailiang Li |
Institute of Mathematics, University of Vienna
A-1090 Vienna, Austria
and Institute of Mathematics, Academia Sinica
Beijing 100080, China
| Chi-Kun Lin |
Department of Mathematics
National Cheng Kung University
Tainan 701, Taiwan
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