On the global existence for a regularized model of viscoelastic non-Newtonian fluid

TL;DR

This paper proves the global existence of weak solutions for a regularized generalized Oldroyd model describing viscoelastic non-Newtonian fluids with shear-dependent viscosity, using advanced mathematical techniques.

Contribution

It introduces a novel approach to establish global solutions for a complex non-Newtonian fluid model with shear-dependent viscosity and nonlinear stress diffusion.

Findings

Proved global existence of weak solutions for the model.

Extended mathematical techniques to handle shear-dependent viscosity.

Validated the model's mathematical well-posedness.

Abstract

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu(\mathbf{D}) \sim |\mathbf{D}|^{p-2}$ ($p>\frac 65$) regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we are able to prove global existence of weak solution to the corresponding system of partial differential equations.