3 years ago

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

Thanh Viet Phan

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.

Publisher URL: https://link.springer.com/article/10.1007/s40306-018-0298-4

DOI: 10.1007/s40306-018-0298-4

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