Well-posedness for the FENE dumbbell model of polymeric flows

We prove local and global well-posedness for the FENE dumbbell model for a very general class of potentials. Indeed, in prior local or global well-posedness results, conditions on the strength of the singularity (or on the parameter b) were made. Here we give a proof in the general case. We also prove global existence results if the data is small or if we restrict to the co-rotational model in dimension 2.