Analysis of a viscoelastic phase separation model

Abstract A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological terms. By construction, the consistent with second law of thermodynamics. We study well-posedness in two space dimensions, i.e., existence weak solutions, weak-strong uniqueness principle, and stability respect to perturbations, which proven means relative energy estimates. Our numerical simulations good agreement physical experiments. Furthermore, qualitative mesoscopic observed.