Stability of arbitrary plane shear flows of viscoelastic fluids with fading memory

By appropriate choosing the time scale, any fluid within a class described by Coleman and Noll [6] will have rapidly fading memory. For this class of fluids equations are derived which govern the perturbations of arbitrary plane shear flows. These equations contain the equations of Becker [3] as a special case. On the basis of them it is shown that for large enough shear rate the local stress power generated by the perturbations is non-positive. Results relating to the stress power obtained by Akbay and Sponagel [2] on the basis of Becker's [3] equations are placed in context.