Optimal Control of a Semidiscrete Cahn-Hilliard-Navier-Stokes System with Non-Matched Fluid Densities
Please always quote using this URN:urn:nbn:de:0296-matheon-13516
- This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instance of a variational inequality of fourth order and the Navier--Stokes equation. By proposing a suitable time-discretization, energy estimates are proved and the existence of solutions to the primal system and of optimal controls is established for the original problem as well as for a family of regularized problems. The latter correspond to Moreau--Yosida type approximations of the double-obstacle potential. The consistency of these approximations is shown and first order optimality conditions for the regularized problems are derived. Through a limit process, a stationarity system for the original problem is established which is related to a function space version of C-stationarity.
Author: | Micheal Hintermüller, Tobias Keil, Donat Wegner |
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URN: | urn:nbn:de:0296-matheon-13516 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2015/12/23 |
Release Date: | 2015/12/23 |
Institute: | Humboldt-Universität zu Berlin |
Project: | C Energy and Materials (Production) / C-SE5 Optimal design and control of optofluidic solar steerers and concentrators |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations |
Preprint Number: | 1090 |