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The steady motion of viscoelastic fluids is investigated in a three-dimensional exterior domain. Results concerning existence, uniqueness and asymptotic behaviour are obtained using appropriately constructed function spaces in which the elements are defined as a sum of the main asymptotic term and of the remainder living in a proper weighted Sobolev space. The equations are written as a coupled system that, at the first stage, can be studied as two linear problems composed of a Stokes system and a transport equation. Finally, a standard contraction argument provides existence and uniqueness of solutions for the original nonlinear coupled set of equations, when the data are sufficiently small.

Asymptotic behaviour at infinity of three-dimensional steady viscoelastic flows