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.
"Existence results for steady flow of weakly compressible viscoelastic fluids with a differential constitutive law." Differential Integral Equations 12 (5) 741 - 772, 1999.