Steady Motions of Viscoelastic Fluids in Three-Dimensional Exterior Domains. Existence, Uniqueness and Asymptotic Behaviour

Abstract

. We study systems of nonlinear partial differential equations governing the steady motion of certain viscoelastic non‐Newtonian fluids around a rigid body \({\cal B}\subset\real^{3}\). Considering the equations in a suitably decomposed form, we obtain, for small and sufficiently regular data, existence of a unique solution using a fixed‐point argument in an appropriate functional setting. This setting contains also the asymptotic decay of the solution. Our model equations include the second‐grade and the Maxwell fluid.