Journal of Convex Analysis 32 (2025), No. 4, 1159--1198
Copyright Heldermann Verlag 2025
Existence of Optimal and ε-Optimal Controls for the Stochastic Cahn-Hilliard Navier-Stokes System
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
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.
Keywords: Cahn-Hilliard Navier-Stokes, epsilon-optimal control, optimal feedback control, stochastic evolution equation, stochastic analysis.
MSC: 76D99, 76M35, 93B52, 93E20.
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