  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 $\mathcal{D}\subset \mathbb{R}^2$. It is shown
that, there exists a finite constant $a^*$, denoting mainly the critical number
of bosons in the system, such that the least energy $e(a)$ admits minimizers if
and only if $0<a<a^*$, no matter the trapping potential $V(x)$ rotates at any
velocity $\Omega\geq0$. This is quite different from the rotating BECs in the
whole plane case, where the existence conclusions depend on the value of
$\Omega$ (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 $a\nearrow
a^*$.
