Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model

Abstract

In this article, we investigate an optimal control problem for the coupled system of partial differential equations describing the steady-state flow of a corotational-type Oldroyd fluid through a bounded 3D (or 2D) domain. The control function is included in Dirichlet boundary conditions for the velocity field; in other words, we consider a model of inflow–outflow control. The main result is a theorem that states sufficient conditions for the solvability of the corresponding optimization problem in the set of admissible weak solutions. Namely, we establish the existence of a weak solution that minimizes the cost functional under given constraints on controls and states.

Keywords

• optimal control problem
• Dirichlet boundary control
• corotational Oldroyd model
• viscoelastic fluid
• diffusive stress
• objective derivative