Steady motions of viscoelastic fluids in three-dimensional exterior domains. Existence, uniqueness and asymptotic behaviour

We study systems of nonlinear partial differential equations governing the steady motion of certain viscoelastic non-Newtonian fluids around a rigid b ody B subset of R-3. Considering the equations in a suitably decomposed for m, we obtain, for small and sufficiently regular data, existence of a uniqu e solution using a fixed-point argument in an appropriate functional settin g. This setting contains also the asymptotic decay of the solution. Our mod el equations include the-second-grade and the Maxwell fluid.