Boundary control problem for stochastic 2d-Navier-Stokes equations

2023/12/10 by Chemetov, Nikolai, Cipriano, Fernanda
#60G15 #60H15 #76B75 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2312.05935

Abstract

We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty, modeled by stochastic non-homogeneous Navier-slip boundary conditions. We show the existence and uniqueness of the solution to the state equation, and prove the existence of an optimal solution to the control problem.

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