Optimal control of Newtonian fluids in a stochastic environment
Abstract
We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the non-homogeneous Navier-slip boundary conditions. After establishing a suitable stability result for the solution of the stochastic state equation, we prove the well-posedness of the stochastic linearized state equation and show that the G\^ateaux derivative of the control-to-state mapping corresponds to the unique solution of the linearized equation. Next, we study the stochastic backward adjoint equation and establish a duality relation between the solutions of the forward linearized equation and the backward adjoint equation. Finally, we derive the first-order optimality conditions.
Keywords
Cite
@article{arxiv.2409.00479,
title = {Optimal control of Newtonian fluids in a stochastic environment},
author = {Nikolai Chemetov and Fernanda Cipriano},
journal= {arXiv preprint arXiv:2409.00479},
year = {2024}
}