On Flows of Viscoelastic Fluids of Oldroyd Type with Wall Slip

We consider the boundary-value problem for the steady isothermal flow of an incompressible viscoelastic liquid of Oldroyd type in a bounded domain with a Navier type slip boundary condition. We prove that under some restrictions on the material constants and the data, there exists a strong solution which is locally unique. The proof is based on a fixed point argument in which the boundary-value problem is decomposed into a transport equation and a Stokes system.