Geodesic
Optimal Control of a Cahn-Hilliard-Navier-Stokes Model with State Constraints
Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1135-1172
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We investigate in this article the Pontryagin's maximum principle for a class of control problems associated with a coupled Cahn-Hilliard-Navier-Stokes model in a two dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity v, coupled with a Cahn-Hilliard model for the order (phase) parameter ϕ. The optimal problems involve a state constraint similar to that considered by G. Wang [Optimal controls of 3-dimensional Navier-Stokes equations with state constraints, SIAM J. Control Optim. 41(2) (2002) 583--606]. We derive the Pontryagin's maximum principle for the control problems assuming that a solution exists. Let us note that the coupling between the Navier-Stokes and the Cahn-Hilliard systems makes the analysis of the control problem more involved.
Classification : 93C05,93B50,93C35
Mots-clés : Two-phase flow model, maximum principle, state constraints 
@article{JCA_2015_22_4_JCA_2015_22_4_a12,
     author = {T. Tachim Medjo},
     title = {Optimal {Control} of a {Cahn-Hilliard-Navier-Stokes} {Model} with {State} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {1135--1172},
     year = {2015},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a12/}
}
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T. Tachim Medjo. Optimal Control of a Cahn-Hilliard-Navier-Stokes Model with State Constraints. Journal of convex analysis, Tome 22 (2015) no. 4, pp. 1135-1172. http://geodesic.mathdoc.fr/item/JCA_2015_22_4_JCA_2015_22_4_a12/