Geodesic
Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle
Lin, Fanghua1  ; Zhang, Ping2 
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 15, 13 p.

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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.

Keywords: Semiclassical limit, Schrödinger equation, compressible Euler equation.

Lin, Fanghua 1 ; Zhang, Ping 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. 
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     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"},
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     pages = {1--13},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2004-2005},
     mrnumber = {2182059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEDP_2004-2005____A15_0/}
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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://geodesic.mathdoc.fr/item/SEDP_2004-2005____A15_0/