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This work is concerned with the study of steady flows of an incompressible viscoelastic fluid of Oldroyd type, with viscosity depending on the second invariant of the rate of deformation tensor in an exterior domain. We establish a result of existence and uniqueness of strong solutions for sufficiently small data and give estimates relating these solutions to those of the corresponding generalized Newtonian fluid.

This work is concerned with the study of steady flows of an incompressible quasi-Newtonian fluid, with viscosity depending on the second invariant of the rate of deformation tensor, in bounded domains. We first establish a result of existence of measure-valued solutions. Next, we prove that under some natural monotonicity conditions, these solutions are weak.