Existence of Optimal and ε-Optimal Controls for the Stochastic Cahn-Hilliard Navier-Stokes System

Raoul D. Ayissi; Gabriel Deugoué; J. Ngandjou Zangue; T. Tachim Medjo

Abstract

We study in this article a stochastic version of a coupled of the Cahn-Hilliard Navier-Stokes model in two dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard model for the order (phase) parameter. We prove the existence of optimal and ε-optimal controls for the stochastic Cahn-Hilliard Navier-Stokes model.

Author information

Contact details are reproduced from the original publication and may be historical.

Raoul D. Ayissi

Department of Mathematics, Faculty of Science, University of Yaoundé 1, Cameroon

raoulayissi@yahoo.fr

Gabriel Deugoué

Department of Mathematics and Computer Science, University of Dschang, Cameroon

agdeugoue@yahoo.fr

J. Ngandjou Zangue

(1) Department of Mathematics, Faculty of Science, University of Yaoundé 1, Cameroon
(2) Department of Mathematics and Computer Science, University of Dschang, Cameroon

ngandjoujosue@gmail.com

T. Tachim Medjo

Dept. of Mathematics and Statistics, Florida International University, Miami, U.S.A.

tachimt@fiu.edu

Keywords

Cahn-Hilliard Navier-Stokes
epsilon-optimal control
optimal feedback control
stochastic evolution equation
stochastic analysis

Mathematics Subject Classification

76D99, 76M35, 93B52, 93E20

Suggested citation

R. D. Ayissi, G. Deugoué, J. N. Zangue, T. T. Medjo. “Existence of Optimal and ε-Optimal Controls for the Stochastic Cahn-Hilliard Navier-Stokes System.” Journal of Convex Analysis 32 (2025), No. 4, 1159–1198.