Inflow boundary conditions for steady flow of viscoelastic fluids with differential constituitive laws

We prove an existence result for steady flows through a strip which can be regarded as a perturbation of rigid motion.The fluid is viscoelastic with a differential constitutive law, e.g., an upper convected Maxwell model.Particular emphasis is focussed on the question which boundary conditions need to be imposed at the inflow boundary to make the problem well-posed.