This contribution deals with a model for viscoelastoplastic two-phase flows of Cahn–Hilliard type. We present the modeling framework for the flow, the notion of a generalized solution, namely the so-called dissipative solution, and the key ideas of the existence proof. With the help of the dissipative solution, we explore the existence of generalized solutions both for a regularized system and a system, which is used in geoscientific applications.
Cheng et al. (Thu,) studied this question.