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

2018/09/25 by Tania Biswas, Biswas, Tania, Sheetal Dharmatti +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1809.10297

openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Maximum Principle and Data Assimilation Problem for the Optimal Control\n Problems Governed by 2D Nonlocal Cahn-Hillard-Navier-Stokes Equations

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