  This paper establishes the existence of smooth solutions for the Doi-Edwards
rheological model of viscoelastic polymer fluids in shear flows. The problem
turns out to be formally equivalent to a K-BKZ equation but with constitutive
functions spanning beyond the usual mathematical framework. We prove, for small
enough initial data, that the solution remains in the domain of hyperbolicity
of the equation for all $t \geq 0$.

Analysis of PDEs