WIAS Preprint No. 2036, (2014)

Optimal distributed control of a nonlocal Cahn--Hilliard/Navier--Stokes system in 2D


  • Frigeri, Sergio Pietro
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

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.

Appeared in

  • SIAM J. Control Optim., 54 (2016), pp. 221 -- 250.

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