Optimal control of steady second grade fluids with Dirichlet boundary conditions

TL;DR

This paper studies optimal control problems for steady second grade fluid flows with fixed boundary conditions, establishing existence, deriving optimality conditions, and analyzing behavior as viscoelastic effects diminish.

Contribution

It introduces a comprehensive analysis of optimal control for second grade fluids, including existence proofs, optimality conditions, and asymptotic behavior as the viscoelastic parameter approaches zero.

Findings

Existence of optimal solutions established

Necessary optimality conditions derived

Asymptotic analysis as viscoelastic parameter tends to zero

Abstract

We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary optimality conditions and analyze its asymptotic behavior when the viscoelastic parameter tends to zero.