  In this paper we mainly investigate the Cauchy problem of the finite
extensible nonlinear elastic (FENE) dumbbell model with dimension $d\geq2$. We
first proved the local well-posedness for the FENE model in Besov spaces by
using the Littlewood-Paley theory. Then by an accurate estimate we get a
blow-up criterion. Moreover, if the initial data is perturbation around
equilibrium, we obtain a global existence result. Our obtained results
generalize recent results in [8].
