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Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain

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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.

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Authors and Affiliations

  1. Courant Institue, 251 Mercer street, New York, NY, 10012, U.S.A.

    Fanghua Lin

  2. Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing, 100080, China

    Ping Zhang

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  1. Fanghua Lin
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  2. Ping Zhang
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Correspondence to Ping Zhang.

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Communicated by L.C. Evans

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Lin, F., Zhang, P. Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain. Arch. Rational Mech. Anal. 179, 79–107 (2006). https://doi.org/10.1007/s00205-005-0383-4

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  • DOI: https://doi.org/10.1007/s00205-005-0383-4

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