The Asymptotic Behaviour of Oldroyd-B Fluids is Almost Newtonian

Abstract

Consider a viscoelastic fluid of Oldroyd-B type. It is shown that its stress tensor $\tau$ and its Newtonian deformation tensor $D(u)$ decay at the same rate, while the elastic part $\epsilon =\tau -2\omega D(u)$ decays faster. As a consequence, the stress tensor of a viscoelastic fluid exhibits an almost Newtonian behaviour for large times.

Updated version with corrections and additions regarding references [16] and [17]