Global stability of Oldroyd-B fluids in plane Couette flow

We prove conditions for global nonlinear stability of Oldroyd-B viscoelastic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude of the polymer perturbations from their steady-state values. The conditions for global stability extend, in a physically natural manner, classical results on global stability of Newtonian Couette flow.