Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

• Published in: Analysis (Wiesbaden) Vol. 40; no. 3; pp. 127 - 150
• Main Authors: Biswas, Tania, Dharmatti, Sheetal, Mohan, Manil T.
• Format: Journal Article
• Language: English
• Published: De Gruyter Oldenbourg 01.08.2020
• Subjects: 35Q35; 49J20; 76D03; necessary and sufficient optimality conditions; nonlocal Cahn–Hilliard–Navier–Stokes systems; Optimal control; Pontryagin maximum principle

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 cont...