On the Doi-Edwards and K-BKZ rheological models for polymer fluids: an   existence result for shear flows
  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 $t \geq 0$. 
Ionel Sorin Ciuperca, Arnaud Heibig, Liviu Iulian Palade
math.AP