Liu, Hailiang; Tadmor, Eitan Semiclassical limit of the nonlinear Schrödinger-Poisson equation with subcritical initial data. (English) Zbl 1166.35374 Methods Appl. Anal. 9, No. 4, 517-531 (2002). Summary: We study the semi-classical limit of the nonlinear Schrodinger-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 [Indiana Univ. Math. J. 50, Spec. Iss., 109–157 (2001; Zbl 0989.35110)], 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. Cited in 8 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35B25 Singular perturbations in context of PDEs PDF BibTeX XML Cite \textit{H. Liu} and \textit{E. Tadmor}, Methods Appl. Anal. 9, No. 4, 517--531 (2002; Zbl 1166.35374) Full Text: DOI