Asymptotic behaviour,with respect to the isothermal compressibility coefficient,for steady flows of weakly compressible viscoelastic fluids

Abstract

In this paper, we study the behaviour, in terms of compressibility, of steady flows of weakly compressible viscoelastic fluids having a differential constitutive law. The models considered here are Jeffreys' and Maxwell's. In both cases, we establish the existence of an asymptotic expansion in the neighbourhood of the steady incompressible fluid flow, with respect to the vanishing isothermal compressibility coefficient.