Existence results for steady flow of weakly compressible viscoelastic fluids with a differential constitutive law

Abstract

In this paper we study flows of viscoelastic weakly compressible fluids having a differential constitutive equation. In both cases, Jeffreys and Maxwell type constitutive equations, we establish a result of existence and uniqueness of solutions. We also show that, when the compressibility goes to zero, then the weakly compressible steady solution goes to the incompressible one.