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

Well-posedness for the FENE dumbbell model of polymetric flows in Besov spaces