Blow-up Profile of the Focusing Gross-Pitaevskii Minimizer Under Self-Gravitating Effect

被引：0
作者：
Thanh Viet Phan
机构：
[1] Ton Duc Thang University,Applied Analysis Research Group, Faculty of Mathematics and Statistics
来源：
Acta Mathematica Vietnamica | 2020年 / 45卷
关键词：
Bose-Einstein condensate; Self-gravitating effect; Concentration-compactness method; Blow-up profile; Gagliardo-Nirenberg inequality; 35Q40; 46N50;
D O I：
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学科分类号：
摘要：
We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an external potential and an interaction potential containing both the short-range attractive self-interaction and the long-range self-gravitating effect. We prove the existence of minimizers and analyze their behavior when the strength of the attractive interaction converges to a critical value. The universal blow-up profile is the unique optimizer of a Gagliardo-Nirenberg interpolation inequality.
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页码：611 / 634
页数：23
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