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

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 ex...

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Bibliographic Details
Published in:Electronic journal of differential equations 2003-09, Vol.2003 (93), p.1-17
Main Authors: Hailiang Li, Chi-Kun Lin
Format: Article
Language:English
Subjects:
Euler-Poisson system
quantum hydrodynamics
quasilinear symmetric hyperbolic system
Schrodinger-Poisson system
semiclassical limit
WKB expansion
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Summary: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.
ISSN:1072-6691