Existence and weak-strong uniqueness for global weak solutions for the viscoelastic phase separation model in three space dimensions

TL;DR

This paper proves the global existence of weak solutions for a three-dimensional viscoelastic phase separation model, addressing both regular and degenerate cases with different potentials and mobilities.

Contribution

It establishes the first comprehensive proof of global weak solutions for this complex model in three dimensions, including degenerate cases with logarithmic potentials.

Findings

Global weak solutions exist for regular polynomial potentials.

Weak solutions also exist for degenerate cases with logarithmic potentials.

The relative energy method is effective in proving existence.

Abstract

The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relative energy concept provided by [3]. We consider the case of regular polynomial-type potentials and positive mobilities, as well as the degenerate case with logarithmic potential and vanishing mobility.