Optimal control of hemivariational inequalities for nonstationary Navier–Stokes equations. (4th May 2022)

• Record Type: Journal Article
• Authors: Chadli, O.; Mohapatra, R. N.
• Is Part Of: Optimization. Volume 71:Number 5(2022)
• Page Start: 1357
• Page End: 1388
• Publication Date: 2022-05-04
• Subjects: Navier–Stokes -- nonmonotone boundary conditions -- optimal control -- equilibrium problems -- hemivariational inequalities; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1836638
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Optimal control of nonstationary Navier–Stokes equations is studied with nonlinear boundary conditions described by the Clarke subdifferential. Precisely, we aim at minimizing a general functional for a control problem whose state is a solution to a boundary value problem depending on the control itself. Accordingly, the lower level problem is expressed by a hemivariational inequality associated with a nonconvex nonsmooth locally Lipschitz superpotential. The existence of solutions to our problem is then shown via a convergence scheme based on mixed equilibria and a stability result with respect to variations on the control for the dynamic state control system associated with the main control problem.