Finite amplitude stability of internal steady flows of the Giesekus viscoelastic rate-type fluid

Using a Lyapunov type functional constructed on the basis of thermodynamical arguments we investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. Using the functional we derive bounds on the Reynolds and the Weissenberg number that guarantee the unconditional asymptotic stability of the corresponding steady internal flow, wherein the distance between the steady flow field and the perturbed flow field is measured with the help of the Bures--Wasserstein distance between positive definite matrices. The application of the theoretical results is documented in the finite amplitude stability analysis of Taylor--Couette flow.
Comment: This version of the manuscript shows how to introduce a metric on the underlying state space and how to prove asymptotic stability using this metric