REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT

Abstract : We consider compressible viscoelastic fluids satisfying the Oldroyd constitutive law. We prove the local existence (and uniqueness) of flows by a classical fixed point argument. We also prove some global properties of the solutions. In particular, we obtain some a priori estimates which are uniform in the Mach number and prove global existence of weakly compressible fluids flows. We show that weakly compressible flows with well-prepared initial data converge to incompressible ones when the Mach number converges to zero.