| Abstract: |
| We consider an optimal control problem for a two-dimensional Navier-Stokes-Cahn-Hilliard system arising in the modeling of fluid-membrane interaction. The fluid dynamics is governed by the incompressible Navier-Stokes equations, which are nonlinearly coupled with a sixth-order Cahn-Hilliard type equation representing the deformation of a flexible membrane through a phase-field variable. We introduce an external forcing term acting on the fluid as the control variable. Then we seek to minimize a tracking-type cost functional, demonstrating the existence of an optimal control and deriving the associated first-order necessary optimality conditions. |
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