2023/05/04 by Bag, Manika, Biswas, Tania, Dharmatti, Sheetal
#49J20 #49J50 #76B99 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2305.02501
In this work, we study an optimal boundary control problem for a Cahn - Hilliard -Navier-Stokes (CHNS) system in a two dimensional bounded domain. The CHNS system consists of a Navier-Stokes equation governing the fluid velocity field coupled with a convective Cahn - Hilliard equation for the relative concentration of the fluids. An optimal control problem is formulated as the minimization of a cost functional subject to the controlled CHNS system where the control acts on the boundary of the Navier-Stokes equations. We first prove that there exists an optimal boundary control. Then we establish that the control-to-state operator is Frechet differentiable and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint system.