Global nonlinear stability of Oldroyd-B fluids in plane Couette flow

This talk will give a rigorous proof of global nonlinear stability for Oldroyd-B fluids in plane Couette flow. Specifically, we derive conditions under which perturbations of arbitrary magnitude must decay asymptotically, which naturally extend classical results for Newtonian fluids to the non-Newtonian setting. The challenge of performing nonlinear stability analysis for viscoeasltic flows is in finding an appropriate quantification of both perturbations from a base-state. To this end, we introduce a new measure, the perturbation entropy, which generalises the notion of relative entropy and gives a probabilistic measure of the deviation of the polymer configuration tensor from its steady distribution. We will show that at any Reynolds number lower than the Newtonian energy stability limit, there exists a range of polymer densities and Weissenberg numbers for which the Oldroyd-B viscoelastic model is also nonlinearly stable.