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Profiles 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 Cauchy problem for Gross-Pitaevskii equation. In terms of Merle and Raphaël’s arguments as well as Carles’ transformation, the limiting profiles of blow-up solutions are obtained. In addition, the nonexistence of a strong limit at the blow-up time and the existence of L 2 profile outside the blow-up point for the blow-up solutions are obtained.

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Authors and Affiliations

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

    Shi-hui Zhu

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

    Jian Zhang

Authors
  1. Shi-hui Zhu
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  2. Jian Zhang
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Correspondence to Shi-hui Zhu.

Additional information

Supported by the National Natural Science Foundation of China (No. 10771151, No. 10747148).

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Zhu, Sh., Zhang, J. Profiles of blow-up solutions for the Gross-Pitaevskii equation. Acta Math. Appl. Sin. Engl. Ser. 26, 597–606 (2010). https://doi.org/10.1007/s10255-010-0027-9

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  • DOI: https://doi.org/10.1007/s10255-010-0027-9

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