Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case

The aim of this paper is to prove global in time existence of weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples the diffusive interface model with the Peterlin-Navier-Stokes equations for viscoelastic fluids. To obtain the global in time existence of weak solutions we consider appropriate approximations by solutions of the viscoelastic phase separation with a regular potential and build on the corresponding energy and entropy estimates.