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Optimal control of a semidiscrete Cahn-Hilliard-Navier-Stokes system with non-matched fluid densities

Submission Status:in press
  • 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 instant 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 with respect to the regularization parameter, a stationarity system for the original problem is established. The resulting system corresponds to a function space version of C-stationarity which is a special notion of stationarity for MPECs.
Metadaten
Author:Tobias Keil, Michael Hintermüller, Donat Wegner
Parent Title (English):SIAM Journal on Control and Optimization
Document Type:Article
Language:English
Date of Publication (online):2017/08/25
Date of first Publication:2017/08/29
Release Date:2017/08/29
Volume:55
First Page:1954
Last Page:1989
Institutes:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02