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|Title:||Optimal distributed control of two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems with degenerate mobility and singular potential|
|Authors:||Frigeri, Sergio; Grasselli, Maurizio; Sprekels, Jürgen|
|Published in:||Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2473, ISSN 2198-5855|
|Publisher:||Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik|
|Abstract:||In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the NavierStokes equations, nonlinearly coupled with a convective nonlocal CahnHilliard equation. The system rules the evolution of the (volume-averaged) velocity u of the mixture and the (relative) concentration difference ' of the two phases. The aim of this work is to study an optimal control problem for such a system, the control being a time-dependent external force v acting on the fluid. We first prove the existence of an optimal control for a given tracking type cost functional. Then we study the differentiability properties of the control-to-state map v 7! [u; '], and we establish first-order necessary optimality conditions. These results generalize the ones obtained by the first and the third authors jointly with E. Rocca in . There the authors assumed a constant mobility and a regular potential with polynomially controlled growth. Here, we analyze the physically more relevant case of a degenerate mobility and a singular (e.g., logarithmic) potential. This is made possible by the existence of a unique strong solution which was recently proved by the authors and C. G. Gal in .|
|Keywords:||Navier–Stokes equations; nonlocal Cahn–Hilliard equations; degenerate mobility; incompressible binary fluids; phase separation; distributed optimal control; first-order necessary optimality conditions|
|License:||This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.|
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
|Appears in Collections:||Mathematik|
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