Steady-state flow of a shear-thinning liquid in an unbounded pipeline system

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