Abstract
AbstractWe investigate in this article Pontryagin's maximum principle for a class of control problems associated with a 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 . We derive 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.
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