Acta Mathematica Vietnamica
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Blow-up Profile of the Focusing Gross-Pitaevskii Minimizer Under Self-Gravitating Effect
Thanh Viet Phanpp. 611-634
Abstract
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.