Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems

Hailiang Li; Chi Kun Lin

Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems

Hailiang Li^*
, Chi Kun Lin

^*Corresponding author for this work

University of Vienna
CAS - Institute of Applied Mathematics
National Cheng Kung University

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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 Schrödinger-Poisson system for a fixed re-scaled Planck constant.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Electronic Journal of Differential Equations
Volume	2003
Publication status	Published - 8 Sept 2003
Externally published	Yes

Keywords

Euler-Poisson system
Quantum hydrodynamics
Quasilinear symmetric hyperbolic system
Schrödinger-Poisson system
Semiclassical limit
WKB expansion

Cite this

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title = "Semiclassical limit and well-posedness of nonlinear Schr{\"o}dinger-Poisson systems",

abstract = "This paper concerns the well-posedness and semiclassical limit of nonlinear Schr{\"o}dinger-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 Schr{\"o}dinger-Poisson system for a fixed re-scaled Planck constant.",

keywords = "Euler-Poisson system, Quantum hydrodynamics, Quasilinear symmetric hyperbolic system, Schr{\"o}dinger-Poisson system, Semiclassical limit, WKB expansion",

author = "Hailiang Li and Lin, \{Chi Kun\}",

year = "2003",

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language = "English",

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AU - Li, Hailiang

AU - Lin, Chi Kun

PY - 2003/9/8

Y1 - 2003/9/8

N2 - 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 Schrödinger-Poisson system for a fixed re-scaled Planck constant.

AB - 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 Schrödinger-Poisson system for a fixed re-scaled Planck constant.

KW - Euler-Poisson system

KW - Quantum hydrodynamics

KW - Quasilinear symmetric hyperbolic system

KW - Schrödinger-Poisson system

KW - Semiclassical limit

KW - WKB expansion

UR - https://www.scopus.com/pages/publications/3042628487

M3 - Article

AN - SCOPUS:3042628487

SN - 1072-6691

VL - 2003

SP - 1

EP - 17

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems

Abstract

Keywords

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