Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model

TL;DR

This paper investigates the three-dimensional Peterlin viscoelastic model, establishing the existence of weak solutions and a conditional weak-strong uniqueness result using advanced mathematical techniques.

Contribution

It provides the first rigorous proof of weak solutions and weak-strong uniqueness for this complex viscoelastic model.

Findings

Existence of weak solutions proven.

Conditional weak-strong uniqueness established.

Application of mixed Galerkin and semigroup methods.

Abstract

In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach we prove the existence of a weak solutions. Further combining parabolic regularity with the relative energy method we derive a conditional weak-strong uniqueness result.