On the Optimal Control of a Class of Non-Newtonian Fluids

TL;DR

This paper investigates optimal control problems for non-Newtonian fluids described by generalized Navier-Stokes equations with shear-dependent viscosity, establishing existence results for solutions in both 2D and 3D domains.

Contribution

It introduces a broad class of viscosity functions, including shear-thinning and shear-thickening, and proves the existence of optimal controls for these complex fluid systems.

Findings

Existence of optimal controls for shear-dependent viscosity fluids

Applicable to both 2D and 3D domains

Includes a wide class of viscosity functions

Abstract

We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions including shear-thinning and shear-thickening behavior. We prove an existence result for such class of optimal control problems.