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 language | English (US) |
---|---|
Pages (from-to) | 79-107 |
Number of pages | 29 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 179 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2006 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering