Optimal control of 3D Navier-Stokes-Voigt equations for convex control constraints

Cung The Anh; Vu Hai Son

doi:10.3934/eect.2024056

Article Contents

2025, Volume 14, Issue 2: 313-338. Doi: 10.3934/eect.2024056

This issue Previous Article On stability and regularity of solutions to generalized Rayleigh-Stokes equations involving delays in Hilbert scales Next Article Uniformly exponentially stable finite-difference model reduction of heat and piezoelectric beam interactions with static or hybrid feedback controllers

Optimal control of 3D Navier-Stokes-Voigt equations for convex control constraints

Cung The Anh^1, , and
Vu Hai Son^1,

1.
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

^*Corresponding author: Cung The Anh
^*Corresponding author: Cung The Anh

Received: March 2024

Revised: October 2024

Early access: October 16, 2024

Published online: October 16, 2024

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02–2023.29.

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Abstract

We study a distributed optimal control problem for Navier-Stokes-Voigt equations in three-dimensional bounded domains with convex control constraints and a general cost functional. We prove the existence of optimal solutions, the first-order necessary optimality conditions, and the second-order sufficient optimality conditions as well as the Lipschitz stability of optimal solutions with respect to the initial data.

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Mathematics Subject Classification: 49J20, 49K20, 49K40, 76D55, 35Q35.

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