Abstract
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) |
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Pages (from-to) | 39-59 |
Number of pages | 21 |
Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
Volume | 115 |
Issue number | 1-2 |
DOIs | |
State | Published - 1990 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics