Time Optimal Control Problem of the 3D Navier-Stokes-α Equations. (27th May 2022)

• Record Type: Journal Article
• Authors: Son, Dang Thanh; Thuy, Le Thi
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 6(2022)
• Page Start: 667
• Page End: 697
• Publication Date: 2022-05-27
• Subjects: 3D Navier-Stokes-α equations -- time optimal control -- existence -- necessary optimality conditions -- sufficient optimality conditions; 35B41 -- 35Q30 -- 37L30 -- 35D05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2055062
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we study an optimal control problem for the three-dimensional Navier-Stokes- α equations in bounded domains with Dirichlet boundary conditions, where the time needed to reach a desired state plays an essential role. We first prove the existence of optimal solutions. Then we establish the first-order and second-order necessary optimality conditions, and the second-order sufficient optimality conditions. The second-order optimality ones obtained in the paper seem to be optimal in the sense that the gap between them is minimal.