Abstract
This document studies the nonlinear stability of discontinuous steady states of a model initial-boundary value problem in one space dimension for incompressible, isothermal shear flow of a non-Newtonian fluid driven by a constant pressure gradient. The non-Newtonian contribution to the shear stress is assumed to satisfy a simple differential constitutive law. The key feature is a non-monotone relation between the total steady shear stress and shear strain- rate that results in steady states having, in general, discontinuities in the strain rate. It is shown that every solution tends to a steady state as t approaches limit of infinity, and we identify steady states that are stable.
Sponsored in part by Grants AFOSR-87-0191, NSF-DMS87-12058, NSF-DMS86-20303, and NSF-DMS87-16132.