The Asymptotic Behaviour of Oldroyd-B Fluids is Almost Newtonian

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.