Semiclassical limit of the Gross-Pitaevskii equation in an exterior domain

Fang-Hua Lin, Ping Zhang

Research output: Contribution to journalArticle

Abstract

In this paper, we study the semiclassical limit of the Gross-Pitaevskii equation (a cubic nonlinear Schrödinger equation) with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches 0.

Original languageEnglish (US)
Pages (from-to)79-107
Number of pages29
JournalArchive for Rational Mechanics and Analysis
Volume179
Issue number1
DOIs
StatePublished - Jan 2006

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Gross-Pitaevskii Equation
Semiclassical Limit
Exterior Domain
Boundary conditions
Compressible Euler Equations
Cubic equation
Slip Boundary Condition
Euler equations
Neumann Boundary Conditions
Nonlinear equations
Unique Solution
Momentum
Nonlinear Equations
Scaling
Singularity
Converge

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Mathematics(all)
  • Mathematics (miscellaneous)

Cite this

Semiclassical limit of the Gross-Pitaevskii equation in an exterior domain. / Lin, Fang-Hua; Zhang, Ping.

In: Archive for Rational Mechanics and Analysis, Vol. 179, No. 1, 01.2006, p. 79-107.

Research output: Contribution to journalArticle

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