  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.
