Stability questions for a fluid of third grade in exterior domains

In this paper we study stability questions concerning non-trivial base flows of a third-grade fluid occupying an exterior domain. The constitutive equations of this continuum were derived earlier by Fosdick and Rajagopal. After stating the problem we establish a weighted energy equality and an a priori estimate for solutions u of the perturbed equations under suitable assumptions on the base flow. Only 'growth' conditions at large distances are assumed. The main result is the stability theorem. After showing an energy equality, we prove that, under mild hypotheses on the basic flow, the perturbation energy is a decreasing function of time, provided the viscosity is sufficiently large. © 1989.