Existence and uniqueness results for non-newtonian fluids of the Oldroyd type in unbounded domains

Abstract. In the paper [13], we give the full system of equations modelling the motion of fuid/viscoelastic solid system, and obtain a differential model like the so-called Oldroyd model for a viscoelastic-fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence of a weak solution is treated.