  In this article, we study the multiplicity, asymptotics and stability of
standing waves with prescribed mass $c>0$ for nonlinear Schr\"odinger equation
with rotation in the mass-supercritical regime arising in Bose-Einstein
condensation. Under suitable restriction on the rotation frequency, by
searching critical points of the corresponding energy functional on the
mass-sphere, we obtain a local minimizer $u_c$ and a mountain pass solution
$\hat{u}_c$. %under suitable assumptions on the related parameters.
Furthermore, we show that $u_c$ is a ground state for small mass $c>0$ and
describe a mass collapse behavior of the minimizers as $c\to 0$, while
$\hat{u}_c$ is an excited state. Finally, we prove that the standing wave
associated with $u_c$ is stable. Notice that the pioneering works
\cite{aMsC,shYZ} imply that finite time blow-up of solutions to this model
occurred in the mass-supercritical setting, therefore, we in the present paper
obtain a new stability result. The main contribution of this paper is to extend
the main results in \cite{JeSp,gYlW} concerning the same model from
mass-subcritical and mass-critical regimes to mass-supercritical regime, where
the physically most relevant case is covered.
