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

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...

Full description

Saved in:
Bibliographic Details
Published inAnalysis (Wiesbaden) Vol. 40; no. 3; pp. 127 - 150
Main Authors Biswas, Tania, Dharmatti, Sheetal, Mohan, Manil T.
Format Journal Article
LanguageEnglish
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
Online AccessGet full text

Cover

More Information
Summary: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 the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.
ISSN:0174-4747
2196-6753
DOI:10.1515/anly-2019-0049