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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 115, Issue 1-2
  • January 1990, pp. 39-59

Stability of discontinuous steady states in shearing motions of a non-Newtonian fluid

  • John A. Nohel (a1), Robert L. Pego (a1) and Athanasios E. Tzavaras (a1)
  • DOI:
  • Published online: 14 November 2011

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.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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