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This paper establishes the existence of smooth solutions for the Doi-Edwardsrheological model of viscoelastic polymer fluids in shear flows. The problemturns out to be formally equivalent to a K-BKZ equation but with constitutivefunctions spanning beyond the usual mathematical framework. We prove, for smallenough initial data, that the solution remains in the domain of hyperbolicityof the equation for all $t \geq 0$.

On the Doi-Edwards and K-BKZ rheological models for polymer fluids: an existence result for shear flows