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...
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| Published in | Analysis (Wiesbaden) Vol. 40; no. 3; pp. 127 - 150 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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De Gruyter Oldenbourg
01.08.2020
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| 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 the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem. |
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| AbstractList | 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. |
| Author | Biswas, Tania Dharmatti, Sheetal Mohan, Manil T. |
| Author_xml | – sequence: 1 givenname: Tania surname: Biswas fullname: Biswas, Tania email: tania9114@iisertvm.ac.in organization: School of Mathematics, Indian Institute of Science Education and Research, Trivandrum (IISER-TVM), Maruthamala PO, Vithura, Thiruvananthapuram, Kerala, 695 551, India – sequence: 2 givenname: Sheetal orcidid: 0000-0001-7011-4108 surname: Dharmatti fullname: Dharmatti, Sheetal email: sheetal@iisertvm.ac.in organization: School of Mathematics, Indian Institute of Science Education and Research, Trivandrum (IISER-TVM), Maruthamala PO, Vithura, Thiruvananthapuram, Kerala, 695 551, India – sequence: 3 givenname: Manil T. orcidid: 0000-0003-3197-1136 surname: Mohan fullname: Mohan, Manil T. email: maniltmohan@ma.iitr.ac.in organization: Department of Mathematics, Indian Institute of Technology (IIT), Roorkee, Haridwar Highway, Roorkee, Uttarakhand 247667, India |
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| Snippet | In this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a... |
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| SubjectTerms | 35Q35 49J20 76D03 necessary and sufficient optimality conditions nonlocal Cahn–Hilliard–Navier–Stokes systems Optimal control Pontryagin maximum principle |
| Title | Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations |
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