Pontryagin's maximum principle and second order optimality condition for optimal control problems for the nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions

In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled non...

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Bibliographic Details
Main Authors Biswas, Tania, Dharmatti, Sheetal, Mohan, Manil T
Format Journal Article
LanguageEnglish
Published 23.02.2018
Subjects
Mathematics - Optimization and Control
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Summary:In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated 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 minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.
DOI:10.48550/arxiv.1802.08413