Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle

Fanghua Lin[1]; Ping Zhang[2]

  • [1] Courant Institute, 251 Mercer Street, New York, NY 10012
  • [2] Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, China.

Séminaire Équations aux dérivées partielles (2004-2005)

  • Volume: 2004-2005, page 1-13

Abstract

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In this paper, we study the semiclassical limit of the 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 .

How to cite

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Lin, Fanghua, and Zhang, Ping. "Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle." Séminaire Équations aux dérivées partielles 2004-2005 (2004-2005): 1-13. <http://eudml.org/doc/11104>.

@article{Lin2004-2005,
abstract = {In this paper, we study the semiclassical limit of the 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 $0.$},
affiliation = {Courant Institute, 251 Mercer Street, New York, NY 10012; Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, China.},
author = {Lin, Fanghua, Zhang, Ping},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Semiclassical limit; Schrödinger equation; compressible Euler equation; semiclassical limit},
language = {eng},
pages = {1-13},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle},
url = {http://eudml.org/doc/11104},
volume = {2004-2005},
year = {2004-2005},
}

TY - JOUR
AU - Lin, Fanghua
AU - Zhang, Ping
TI - Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle
JO - Séminaire Équations aux dérivées partielles
PY - 2004-2005
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2004-2005
SP - 1
EP - 13
AB - In this paper, we study the semiclassical limit of the 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 $0.$
LA - eng
KW - Semiclassical limit; Schrödinger equation; compressible Euler equation; semiclassical limit
UR - http://eudml.org/doc/11104
ER -

References

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