REGULAR FLOWS OF WEAKLY COMPRESSIBLE VISCOELASTIC FLUIDS AND THE INCOMPRESSIBLE LIMIT

摘要

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.