We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier-Stokes system with a convective nonlocal Cahn-Hilliard equation in two dimensions of space. We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in two dimensions / S. Frigeri, E. Rocca, J. Sprekels. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 1095-7138. - 54:1(2016), pp. 221-250. [10.1137/140994800]
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in two dimensions
S. Frigeri;
2016
Abstract
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier-Stokes system with a convective nonlocal Cahn-Hilliard equation in two dimensions of space. We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.
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