Optimal control of non-stationary second grade fluids with Navier-slip boundary conditions

TL;DR

This paper investigates the optimal control of unsteady second grade fluid flows with Navier-slip boundary conditions, establishing existence of solutions and deriving necessary optimality conditions.

Contribution

It introduces a framework for controlling non-stationary second grade fluids with Navier-slip boundaries, including existence proofs and optimality conditions.

Findings

Existence of optimal control solutions established.

Necessary optimality conditions derived.

Framework applicable to non-stationary second grade fluids.

Abstract

We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding necessary optimality conditions.