On some unsteady motions of fluids of second grade. (English) Zbl 0835.76002

Summary: We first study the start-up flow of a fluid of second grade occupying the space above a plate which is impulsively set in motion, and show that previous attempts to solve the problem using Laplace transform techniques are erroneous, and that the inversion of the Laplace transform is far from routine. We then study the problem in which the plate moves with a constant speed or accelaration, or is subject to a constant shear. The differences between these solutions and the corresponding cases in the Navier-Stokes theory are delineated.


76A05 Non-Newtonian fluids
44A10 Laplace transform