SIAM Journal on Control and Optimization, Vol.54, No.1, 221-250, 2016
OPTIMAL DISTRIBUTED CONTROL OF A NONLOCAL CAHN-HILLIARD/NAVIER-STOKES SYSTEM IN TWO DIMENSIONS
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.
Keywords:distributed optimal control;first-order necessary optimality conditions;nonlocal models;integrodifferential equations;Navier-Stokes system;Cahn-Hilliard equation;phase separation