Mv-strong uniqueness for density dependent, non-Newtonian, incompressible fluids

TL;DR

This paper establishes the mv-strong uniqueness of dissipative measure-valued solutions for density-dependent, non-Newtonian incompressible fluids on a flat torus, contributing to the mathematical understanding of such complex fluid systems.

Contribution

It introduces the concept of dissipative measure-valued solutions for these fluids and proves their mv-strong uniqueness, a novel result in this context.

Findings

Existence of dissipative measure-valued solutions

Proof of mv-strong uniqueness for these solutions

Enhanced understanding of non-Newtonian fluid models

Abstract

We consider density dependent, non-Newtonian, incompressible system with the space being flat torus. The viscious stress in the momentum equation is understood through the rheological law and its connection to the proper convex potential. We define the dissipative measure-valued solutions for the aforementioned equations as well as provide a proof of its existence. The main result of this work is the mv-strong uniqueness of the defined solutions.