Existence of Weak Solutions for a Diffuse Interface Model of Non-Newtonian Two-Phase Flows

TL;DR

This paper proves the existence of weak solutions for a phase field model describing two non-Newtonian, incompressible, partly miscible fluids with equal densities, using advanced mathematical techniques for large-time behavior.

Contribution

It introduces a novel application of parabolic Lipschitz truncation to establish weak solution existence in a complex non-Newtonian two-phase flow model.

Findings

Existence of weak solutions for the model

Applicability to large-time scenarios

Use of Lipschitz truncation method

Abstract

We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak solutions for general initial data and arbitrarily large times with the aid of a parabolic Lipschitz truncation method, which preserves solenoidal velocity fields and was recently developed by Breit, Diening, and Schwarzacher.