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

TL;DR

This paper analyzes a viscoelastic phase separation model, introducing a relative energy concept to establish weak-strong uniqueness and providing estimates in two and three dimensions.

Contribution

It develops a novel relative energy framework for the viscoelastic phase separation model, enabling weak-strong uniqueness proofs and estimates in multiple dimensions.

Findings

Proved weak-strong uniqueness using the relative energy method.

Derived estimates for the full model in two dimensions.

Presented conditional estimates for a reduced model in three dimensions.

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.