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Optimal control of a semi-discrete Cahn-Hilliard-Navier-Stokes system
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Wegner, Donat
Published in
SIAM Journal on Control and Optimization, Philadelphia, Pa., 2014, Vol. 52, Issue 1, page 747-772
Publisher version
Document typeJournal Article
Keywords (EN)Cahn-Hilliard-Navier-Stokes system / double-obstacle potential / athematical programming with equilibrium constraints / optimal boundary control / Yosida regularization / C-stationarity
URNurn:nbn:at:at-ubg:3-959 Persistent Identifier (URN)
 The work is publicly available
Optimal control of a semi-discrete Cahn-Hilliard-Navier-Stokes system [0.34 mb]
Abstract (English)

In this paper, the optimal boundary control of a time-discrete Cahn-Hilliard-Navier-Stokes system is studied. A general class of free energy potentials is considered which, in particular, includes the double-obstacle potential. The latter homogeneous free energy density yields an optimal control problem for a family of coupled systems, which result from a time discretization of a variational inequality of fourth order and the Navier--Stokes equation. The existence of an optimal solution to the time-discrete control problem as well as an approximate version is established. The latter approximation is obtained by mollifying the Moreau--Yosida approximation of the double-obstacle potential. First order optimality conditions for the mollified problems are given, and in addition to the convergence of optimal controls of the mollified problems to an optimal control of the original problem, first order optimality conditions for the original problem are derived through a limit process. The newly derived stationarity system is related to a function space version of C-stationarity.