Incompressible limit for compressible viscoelastic flows with large velocity

Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.