Global existence and well-posedness for the FENE dumbbell model of polymeric flows

In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension d≥2. 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 a small perturbation around equilibrium, we obtain a global existence result. Our obtained results generalize and cover recent results in Masmoudi (2008).