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This paper is concerned with the existence and mass concentration behavior ofminimizers for rotating Bose-Einstein condensations (BECs) with attractiveinteractions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shownthat, there exists a finite constant $a^*$, denoting mainly the critical numberof bosons in the system, such that the least energy $e(a)$ admits minimizers ifand only if $0<a<a^*$, no matter the trapping potential $V(x)$ rotates at anyvelocity $\Omega\geq0$. This is quite different from the rotating BECs in thewhole plane case, where the existence conclusions depend on the value of$\Omega$ (cf. \cite[Theorem 1.1]{GLY}). Moreover, by establishing the refinedestimates of the rotation term and the least energy, we also analyze the massconcentration behavior of minimizers in a harmonic potential as $a\nearrowa^*$.

Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains