A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations

Chemetov, Nikolai; Cipriano, Fernanda

http://hdl.handle.net/10362/167686

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Autores

Chemetov, Nikolai

Cipriano, Fernanda

Resumo(s)

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.

Descrição

Funding Information: The work of N.V. Chemetov was also supported by FAPESP (Fundação de Amparo à pesquisa do Estado de São Paulo), project 2021/03758-8, "Mathematical problems in fluid dynamics". Publisher Copyright: © The Author(s) 2024.

Palavras-chave

60G15 60H15 76B75 76D05 Navier-slip boundary conditions Optimal control Stochastic Navier–Stokes equations Control and Optimization Management Science and Operations Research Applied Mathematics