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

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 in [ELT, Indiana Univ.Math.J., 50 (2001), 109-157], 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.

Locations

• Methods and Applications of Analysis - View - PDF