Concentration of blow-up solutions for the Gross-Pitaveskii equation

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 L2{L}^{2} supercritical case. Finally, in the L2{L}^{2} critical case, a delicate limit of blow-up solutions is analyzed.

Keywords

• attractive bose-einstein condensate
• gross-pitaveskii equation
• blow-up solution
• blow-up rate
• concentration
• 35q55
• 81q99