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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
