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December 2002 Semiclassical Limit of the Nonlinear Schr$#x00F6;dinger-Poisson Equation with Subcritical Initial Data
Hailiang Liu, Eitan Tadmor
Methods Appl. Anal. 9(4): 517-532 (December 2002).

Abstract

We study the semi-classical limit of the nonlinear Schr$#x00F6;dinger-Poisson (NLSP) equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown that the isotropic Euler-Poisson equations admit a critical threshold phenomena, where initial data in the sub-critical regime give rise to globally smooth solutions. Consequently, we justify the semi-classical limit for sub-critical NLSP initial data and confirm the validity of the WKB method.

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Hailiang Liu. Eitan Tadmor. "Semiclassical Limit of the Nonlinear Schr$#x00F6;dinger-Poisson Equation with Subcritical Initial Data." Methods Appl. Anal. 9 (4) 517 - 532, December 2002.

Information

Published: December 2002
First available in Project Euclid: 1 September 2009

MathSciNet: MR2006603

Rights: Copyright © 2002 International Press of Boston

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Vol.9 • No. 4 • December 2002
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