Abstract
Abstract We consider the blow-up solutions for the Gross-Pitaveskii equation modeling the attractive Boes-Einstein condensate. First, a new variational characteristic is established by computing the best constant of a generalized Gagliardo-Nirenberg inequality. Then, a lower bound on blow-up rate and a new concentration phenomenon of blow-up solutions are obtained in the L 2 {L}^{2} supercritical case. Finally, in the L 2 {L}^{2} critical case, a delicate limit of blow-up solutions is analyzed.
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