We study 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. We show that every solution tends to a steady state as t→∞, and we identify steady states that are stable.
|Original language||English (US)|
|Number of pages||21|
|Journal||Proceedings of the Royal Society of Edinburgh: Section A Mathematics|
|State||Published - 1990|
ASJC Scopus subject areas