Strong Steady Solutions for a Generalized Oldroyd-B Model with Shear-Dependent Viscosity in a Bounded Domain

Abstract

We study a system of nonlinear partial differential equations governing the motion of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain, with a non-Newtonian viscosity depending on the second invariant of the rate of deformation tensor. Considering the equations in a suitably decomposed form, we establish, for small and suitably regular data, existence of a unique solution using a fixed point argument in an appropriate functional setting. This model includes the classical Oldroyd-B fluid as a particular case.