EXISTENCE AND STABILITY OF STEADY FLOWS OF WEAKLY VISCOELASTIC FLUIDS

We consider steady flows of viscoelastic fluids for which the extrastress tensor is given by a differential constitutive equation and is such that the retardation time is large (weakly viscoelastic fluids). We show the existence of a unique viscoelastic steady flow close to a given Newtonian flow and investigate its linear stability. As an example, we consider the Benard problem for viscoelastic fluids and we prove that there exists a nontrivial linearly stable flow of a weakly viscoelastic fluid in a container heated from below.