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

Nikolai Chemetov () and Fernanda Cipriano ()
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Nikolai Chemetov: University of São Paulo
Fernanda Cipriano: New University of Lisbon

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 29, 1847-1879

Abstract: 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.

Keywords: Stochastic Navier–Stokes equations; Navier-slip boundary conditions; Optimal control; 76B75; 60G15; 60H15; 76D05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02416-3

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