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
@article{SEDP_2004-2005____A15_0,
author = {Lin, Fanghua and Zhang, Ping},
title = {Semiclassical {Limit} of the cubic nonlinear {Schr\"odinger} {Equation} concerning a superfluid passing an obstacle},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:15},
pages = {1--13},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2004-2005},
mrnumber = {2182059},
language = {en},
url = {http://archive.numdam.org/item/SEDP_2004-2005____A15_0/}
}
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:15 PY - 2004-2005 SP - 1 EP - 13 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2004-2005____A15_0/ LA - en ID - SEDP_2004-2005____A15_0 ER -
%0 Journal Article %A Lin, Fanghua %A Zhang, Ping %T Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:15 %D 2004-2005 %P 1-13 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2004-2005____A15_0/ %G en %F SEDP_2004-2005____A15_0
Lin, Fanghua; Zhang, Ping. Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 15, 13 p. http://archive.numdam.org/item/SEDP_2004-2005____A15_0/
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