2024/07/17 by Telma Guerra, Guerra, Telma, Irene Marín-Gayte +3
Computer Science · Engineering · #35Q30 #49K20 #49M41 #65K10 #76D05 #93C95 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2407.12561
openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and control variables. We provide a comprehensive theoretical framework to address the analysis and the derivation of a system of first-order optimality conditions that characterizes the solution of the control problem. We take advantage of an adequate treatment of the Dirichlet control through the study of the reduced functional. Despite the fact that this approach is quite common, a detailed analysis for the case of mixed boundary conditions with is still lacking. Finally, solution-finding algorithms of descent type are proposed and illustrated with several simulations.