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Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains
This paper is concerned with the existence and mass concentration behavior of
minimizers for rotating Bose-Einstein condensations (BECs) with attractive
interactions in a bounded domain . It is shown
that, there exists a finite constant , denoting mainly the critical number
of bosons in the system, such that the least energy admits minimizers if
and only if , no matter the trapping potential rotates at any
velocity . This is quite different from the rotating BECs in the
whole plane case, where the existence conclusions depend on the value of
(cf. \cite[Theorem 1.1]{GLY}). Moreover, by establishing the refined
estimates of the rotation term and the least energy, we also analyze the mass
concentration behavior of minimizers in a harmonic potential as