  We investigate an inflow problem for the multi-dimensional isentropic
compressible Navier-Stokes equations. The fluid under consideration occupies
the exterior domain of unit ball, $\Omega=\{x\in\mathbb{R}^n\,\vert\, |x|\ge
1\}$, and a constant stream of mass is flowing into the domain from the
boundary $\partial\Omega=\{|x|=1\}$. The existence and uniqueness of a
spherically symmetric stationary solution, denoted as
$(\tilde{\rho},\tilde{u})$, is first proved by I. Hashimoto and A. Matsumura in
2021. In this paper, we show that either $\tilde{\rho}$ is monotone increasing
or $\tilde{\rho}$ attains a unique global minimum, and this is classified by
the boundary condition of density. Moreover, we also derive a set of decay
rates for $(\tilde{\rho},\tilde{u})$ which allows us to prove the long time
stability of $(\tilde{\rho},\tilde{u})$ under small initial perturbations using
the energy method. The main difficulty for this is the boundary terms that
appears in the a-priori estimates. We resolve this issue by reformulating the
problem in Lagrangian coordinate system.
