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Limiting profile of blow-up solutions for the Gross-Pitaevskii equation

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Abstract

This paper is concerned with the blow-up solutions of the Gross-Pitaevskii equation. Using the concentration compact principle and the variational characterization of the corresponding ground state, we obtain the limiting profile of blow-up solutions with critical mass in the corresponding weighted energy space. Moreover, we extend this result to small super-critical mass case by the variational methods and scaling technique.

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, 610064, China

    ShiHui Zhu

  2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Jian Zhang

  3. College of Economics, Sichuan Normal University, Chengdu, 610066, China

    XiaoGuang Li

Authors
  1. ShiHui Zhu
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  2. Jian Zhang
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  3. XiaoGuang Li
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Corresponding author

Correspondence to ShiHui Zhu.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10771151) and Scientific Research Fund of Sichuan Provincial Education Department (Grant No. 2006A068)

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Zhu, S., Zhang, J. & Li, X. Limiting profile of blow-up solutions for the Gross-Pitaevskii equation. Sci. China Ser. A-Math. 52, 1017–1030 (2009). https://doi.org/10.1007/s11425-008-0140-x

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  • DOI: https://doi.org/10.1007/s11425-008-0140-x

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