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arXiv · 2312.05935

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

Nikolai Chemetov·Fernanda Cipriano
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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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Nikolai Chemetov, Fernanda Cipriano. 2023-12-10. Boundary control problem for stochastic 2d-Navier-Stokes equations. https://arxiv.org/abs/2312.05935

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