Methods and Applications of Analysis

Volume 9 (2002)

Number 4

Semiclassical Limit of the Nonlinear Schrödinger-Poisson Equation with Subcritical Initial Data

Pages: 517 – 532

DOI: http://dx.doi.org/10.4310/MAA.2002.v9.n4.a3

Authors

Hailiang Liu

Eitan Tadmor

Abstract

We study the semi-classical limit of the nonlinear Schrödinger-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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