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Asymptotic limit of the Gross-Pitaevskii equation with general initial data

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Abstract

This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

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Author notes

  1. Chi-Kun Lin

    Present address: Department of Mathematical Sciences, Xi’an Jiaotong Liverpool University (XJTLU), Suzhou, 215123, China

Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    FuCai Li

  2. Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing, Chiao Tung University, Hsinchu, 30010, China

    Chi-Kun Lin

  3. Department of Mathematics, Cheng Kung University, Tainan, 70101, China

    Kung-Chien Wu

Authors
  1. FuCai Li
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  2. Chi-Kun Lin
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  3. Kung-Chien Wu
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Correspondence to FuCai Li.

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Li, F., Lin, CK. & Wu, KC. Asymptotic limit of the Gross-Pitaevskii equation with general initial data. Sci. China Math. 59, 1113–1126 (2016). https://doi.org/10.1007/s11425-015-5104-3

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  • DOI: https://doi.org/10.1007/s11425-015-5104-3

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