
Journal of Convex Analysis 22 (2015), No. 4, 11351172 Copyright Heldermann Verlag 2015 Optimal Control of a CahnHilliardNavierStokes Model with State Constraints Theodore Tachim Medjo Dept. of Mathematics, Florida International University, University Park, Miami, FL 33199, U.S.A. tachimt@fiu.edu We investigate in this article the Pontryagin's maximum principle for a class of control problems associated with a coupled CahnHilliardNavierStokes model in a two dimensional bounded domain. The model consists of the NavierStokes equations for the velocity v, coupled with a CahnHilliard model for the order (phase) parameter φ. The optimal problems involve a state constraint similar to that considered by G. Wang [Optimal controls of 3dimensional NavierStokes equations with state constraints, SIAM J. Control Optim. 41(2) (2002) 583606]. We derive the Pontryagin's maximum principle for the control problems assuming that a solution exists. Let us note that the coupling between the NavierStokes and the CahnHilliard systems makes the analysis of the control problem more involved. Keywords: Twophase flow model, maximum principle, state constraints. MSC: 93C05,93B50,93C35 [ Fulltextpdf (246 KB)] for subscribers only. 