Steady Flows of Viscoelastic Fluids in Domains with Outlets to Infinity

The equations governing the motion of incompressible viscoelastic fluids of Rivlin—Ericksen and Oldroyd type are investigated in domains with cylindrical and paraboloidal outlets to infinity. For sufficiently small fluxes, prescribed in each outlet, existence and uniqueness of solutions are proven in weighted Hölder spaces. In domains with paraboloidal outlets the solution is obtained as a perturbation of the corresponding Navier—Stokes solution and in domains with cylindrical outlets as a perturbation of a flux carrier, constructed by joining together the exact solutions found in each outlet. These exact solutions are shown to be either rectilinear flows of Poiseuille type or flows composed of a rectilinear and of a transverse secondary component.