Leray-Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress-strain relation

TL;DR

This paper establishes the existence of global weak solutions for a complex fluid model that combines viscoelastic and viscoplastic effects, featuring nonsmooth stress relations and stress diffusion.

Contribution

It introduces a mathematical framework proving the existence of solutions for a fluid model with nonlinear, nonsmooth stress laws and transport dynamics.

Findings

Existence of global-in-time weak solutions.

Solutions satisfy an energy inequality.

Model incorporates nonsmooth dissipation and stress diffusion.

Abstract

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba-Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.