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Dinh-Thi, Nguyen (2020): Blow-up profile of 2D focusing mixture Bose gases. In: Zeitschrift für Angewandte Mathematik und Physik, Vol. 71, No. 3, 81
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We study the collapse of a many-body system which is used to model two-component Bose-Einstein condensates with attractive intra-species interactions and either attractive or repulsive inter-species interactions. Such a system consists a mixture of two different species for N identical bosons in R2, interacting with potentials rescaled in the mean-field manner -N2 beta-1w(sigma)(N beta x), we first show that the leading order of the quantum energy is captured correctly by the Gross-Pitaevskii energy. Secondly, we investigate the blow-up behavior of the quantum energy as well as the ground states when N ->infinity, and either the total interaction strength of intra-species and inter-species or the strengths of intra-species interactions of each component approach sufficiently slowly a critical value, which is the critical strength for the focusing Gross-Pitaevskii functional. We prove that the many-body ground states fully condensate on the (unique) Gagliardo-Nirenberg solution.