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Steady-state flow of a shear-thinning liquid in an unbounded pipeline system
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Giovanni P. Galdi
Published/Copyright:
September 1, 2015
Abstract
We show existence and uniqueness of steady-state solutions to the equations of generalized Newtonian liquids of shear-thinning type in an unbounded region that includes semi-infinite cylinders of constant cross-section (pipeline system). This result is established under the assumption that the datum (flow-rate) is sufficiently small. The main feature of our approach is the proof of a “global compactness” property of the sequence of approximating solutions.
Keywords: Poiseuille flow; non-Newtonian fluids; non-linear elliptic problems; domains with unbounded boundary; Leray's problem
Funding source: NSF
Award Identifier / Grant number: DMS-1311983
Funding source: INdAM
Award Identifier / Grant number: GNAMPA
Received: 2014-11-29
Accepted: 2015-8-14
Published Online: 2015-9-1
Published in Print: 2015-11-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Time delay and Lagrangian approximation for Navier–Stokes flow
- Compressible Navier–Stokes limit of binary mixture of gas particles
- On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations
- A regularity criterion of Serrin-type for the Navier–Stokes equations involving the gradient of one velocity component
- Steady-state flow of a shear-thinning liquid in an unbounded pipeline system
- Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
- On the steady flow of reactive gaseous mixture
- Spectral stability of Prandtl boundary layers: An overview
Keywords for this article
Poiseuille flow;
non-Newtonian fluids;
non-linear elliptic problems;
domains with unbounded boundary;
Leray's problem
Articles in the same Issue
- Frontmatter
- Time delay and Lagrangian approximation for Navier–Stokes flow
- Compressible Navier–Stokes limit of binary mixture of gas particles
- On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations
- A regularity criterion of Serrin-type for the Navier–Stokes equations involving the gradient of one velocity component
- Steady-state flow of a shear-thinning liquid in an unbounded pipeline system
- Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions
- On the steady flow of reactive gaseous mixture
- Spectral stability of Prandtl boundary layers: An overview
