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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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
Keywords
- Gross-Pitaevskii equation
- blow-up solution
- Bose-Einstein condensate
- harmonic potential
- concentration compact principle
- small super-critical mass