Optimal distributed control of a nonlocal Cahn--Hilliard/Navier--Stokes system in 2D
- Frigeri, Sergio Pietro
- Rocca, Elisabetta
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 49J20 49J50 35R09 45K05 74N99
- Distributed optimal control, first-order necessary optimality conditions, nonlocal models, integrodifferential equations, Navier-Stokes system, Cahn-Hilliard equation, phase separation
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.
- SIAM J. Control Optim., 54 (2016), pp. 221 -- 250.