Existence of steady solutions for a general model for micropolar electrorheological fluid flows

TL;DR

This paper proves the existence of steady solutions for a general micropolar electrorheological fluid model using advanced mathematical techniques, without requiring extra conditions on the electric field.

Contribution

It introduces a novel existence proof for solutions to a complex fluid flow model employing weighted Sobolev spaces and Lipschitz truncation, broadening understanding of such fluids.

Findings

Existence of solutions established for the steady micropolar electrorheological fluid model.

No additional assumptions needed on the electric field for the existence proof.

Application of Lipschitz truncation technique in this context.

Abstract

In this paper we study the existence of solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of this particular problem leads naturally to weighted Sobolev spaces. By deploying the Lipschitz truncation technique, we establish the existence of solutions without additional assumptions on the electric field.