Pontryagin's maximum principle for optimal control of the nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions
Tania Biswas, Sheetal Dharmatti, Manil T. Mohan · arXiv (Cornell University) · 2018
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn-Hilliard-Navier-Stokes equations. We prove the existence of an optimal control and then establish the Pontryagin's maximum principle for optimal control of such systems, which gives the first-order necessary conditions of optimality. We characterize the optimal control using the adjoint variable.