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

2018/08/27 by Thanh Viet Phan, Phan, Thanh Viet
Physics and Astronomy · #35Q40 #46N50 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Optical properties and cooling technologies in crystalline materials #Strong Light-Matter Interactions

paper · pdf · doi:10.48550/arxiv.1808.08909

openalex publication_date 2018/08/27 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an\nexternal potential and an interaction potential containing both of the\nshort-range attractive self-interaction and the long-range self-gravitating\neffect. We prove the existence of minimizers and analyze their behavior when\nthe strength of the attractive interaction converges to a critical value. The\nuniversal blow-up profile is the unique optimizer of a Gagliardo-Nirenberg\ninterpolation inequality.\n

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