Second Order Optimality Conditions for Optimal Control Problems Governed by 2D Nonlocal Cahn Hilliard Navier Stokes Equations
Optimization and Control
2018-09-28 v1
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.
Cite
@article{arxiv.1809.10297,
title = {Second Order Optimality Conditions for Optimal Control Problems Governed by 2D Nonlocal Cahn Hilliard Navier Stokes Equations},
author = {Tania Biswas and Sheetal Dharmatti and Manil T Mohan},
journal= {arXiv preprint arXiv:1809.10297},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1803.11337, arXiv:1802.08413