Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes   system in 2D
  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. 
Sergio Frigeri, Elisabetta Rocca, and J\"urgen Sprekels
math.AP