  In this paper, we mainly study global well-posedness and optimal decay rate
for the strong solutions of the compressible co-rotation finite extensible
nonlinear elastic (FENE) dumbbell model. This model is a coupling of the
isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck
equation. We first prove that the FENE dumbbell model admits a unique global
strong solution provided the initial data are close to equilibrium state for
$d\geq 2$. Moreover, for $d\geq3$, we show that optimal decay rates of global
strong solutions by the linear spectral theory and a more precise Hardy type
inequality.
