Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems
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Date
2003-09-08
Authors
Li, Hailiang
Lin, Chi-Kun
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
This paper concerns the well-posedness and semiclassical limit of nonlinear Schrödinger-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.
Description
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 A<sup>∊</sup> ∈ L<sup>∞</sup> ([0, T]; H<sup>s</sup> (ℝ<sup>N</sup>)) should be replaced by |A<sup>∊</sup>| - √C ∈ L<sup>∞</sup> ([0, T]; H<sup>s</sup> (ℝ<sup>N</sup>)). On the fourteenth line of Theorem 2.2, the expression A<sup>∊</sup> should be replaced by |A<sup>∊</sup>| - √C ∈ L<sup>∞</sup> ([0, T]; H<sup>s</sup> (ℝ<sup>N</sup>)).
See last page of this manuscript for details.
Keywords
Schrodinger-Poisson system, Quantum hydrodynamics, Euler-Poisson system, Semiclassical limit, WKB expansion, Quasilinear symmetric hyperbolic system
Citation
Li, H., & Lin, C. K. (2003). Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems. <i>Electronic Journal of Differential Equations, 2003</i>(93), pp. 1-17.
Rights
Attribution 4.0 International