On steady motion of viscoelastic fluid of Oldroyd type

We consider a mathematical model describing the steady motion of a viscoelastic medium of Oldroyd type under the Navier slip condition at the boundary. In the rheological relation, we use the objective regularized Jaumann derivative. We prove the solubility of the corresponding boundary-value problem in the weak setting. We obtain an estimate for the norm of a solution in terms of the data of the problem. We show that the solution set is sequentially weakly closed. Furthermore, we give an analytic solution of the boundary-value problem describing the flow of a viscoelastic fluid in a flat channel under a slip condition at the walls. Bibliography: 13 titles.