Second Order Optimality Conditions for Optimal Control Problems Governed by 2D Nonlocal Cahn Hilliard Navier Stokes Equations

Abstract

In this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn-Hilliard-Navier-Stokes equations. We describe the first order necessary conditions of optimality via Pontryagin's minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

arXiv commentarXiv admin note: text overlap with arXiv:1803.11337, arXiv:1802.08413

References in corpus (3)

• Optimal distributed control of a diffuse interface model of tumor growth
• Maximum Principle and Data Assimilation Problem for the Optimal Control Problems Governed by 2D Nonlocal Cahn-Hillard-Navier-Stokes Equations
• Pontryagin's maximum principle and second order optimality condition for optimal control problems for the nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions