EXISTENCE RESULTS FOR FLOWS OF SLIGHTLY COMPRESSIBLE VISCOELASTIC FLUIDS IN A BOUNDED DOMAIN WITH CORNERS

Abstract

Steady flows of slightly compressible viscoelastic fluids of Oldroyd's type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces [Formula: see text], where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇φ.