Relative energy and weak-strong uniqueness of the two-phase viscoelastic phase separation model

Abstract

The aim of this paper is to analyze a viscoelastic phase separation model. We derive a suitable notion of the relative energy taking into account the non-convex nature of the energy law for the viscoelastic phase separation. This allows us to prove the weak-strong uniqueness principle. We will provide the estimates for the full model in two space dimensions. For a reduced model we present the estimates in three space dimensions and derive conditional relative energy estimates.