On the existence of optimal and ɛ-optimal controls for the stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes system
Article
Ayissi, RD, Deugoué, G, Ngandjou Zangue, J et al. (2026). On the existence of optimal and ɛ-optimal controls for the stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes system
. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 265 10.1016/j.na.2025.114016
Ayissi, RD, Deugoué, G, Ngandjou Zangue, J et al. (2026). On the existence of optimal and ɛ-optimal controls for the stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes system
. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 265 10.1016/j.na.2025.114016
In this paper, we study a feedback optimal control problem for the stochastic nonlocal Cahn–Hilliard–Navier–Stokes model in a two-dimensional bounded domain. The model consists of the stochastic Navier–Stokes equations for the velocity, coupled with a nonlocal Cahn-Hilliard system for the order (phase) parameter. We prove the existence of an optimal feedback control for the stochastic nonlocal Cahn–Hilliard-Navier-Stokes system. Moreover using the Galerkin approximation, we show that the optimal cost can be approximated by a sequence of finite dimensional optimal costs.
