Science in China Series A: Mathematics

, Volume 52, Issue 5, pp 1017–1030 | Cite as

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

Article
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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.

Keywords

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

MSC(2000)

35B35 35Q53 
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Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.College of MathematicsSichuan UniversityChengduChina
  2. 2.College of Mathematics and Software ScienceSichuan Normal UniversityChengduChina
  3. 3.College of EconomicsSichuan Normal UniversityChengduChina

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