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arXiv · 1808.08909

Blow-up profile of the focusing Gross-Pitaevskii minimizer under self-gravitating effect

Thanh Viet Phan
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Abstract

We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an external potential and an interaction potential containing both of 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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Thanh Viet Phan. 2018-08-27. Blow-up profile of the focusing Gross-Pitaevskii minimizer under self-gravitating effect. https://arxiv.org/abs/1808.08909

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