## 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 |

### Bibliographical note

Funding Information:Supported by the U.S. Army Research Office under Grant DAAL03-87-K-0036 and DAAL03-88-K-0185, the Air Force Office of Scientific Research under Grant AFOSR-87-0191; the National Science Foundation under Grants DMS-8712058, DMS-8620303, DMS-8716132, and a NSF Post Doctoral Fellowship (Pego).

## ASJC Scopus subject areas

- General Mathematics