Stationary non-Newtonian fluid flows in channel-like and pipe-like domains

This paper is concerned with stationary non-Newtonian fluid in an unbounded domain which geometrically is channel-like in two dimensions or axisymmetric pipe-like in three. The flow satisfies no-slip boundary conditions, and behaves as Poiseuille flow at infinity. Existence and uniqueness are proved under the assumption of a large kinematic viscosity. The results apply to a family of models including second-order, Maxwell and Oldroyd-B fluids. For second-order fluids, the existence and uniqueness results are extended to the case when the boundary has corner points.