Article In: scopus
Steady Navier–Stokes equations with regularized directional do-nothing boundary condition: optimal boundary control for a velocity tracking problem
Applied Mathematics and Optimization
— 2025 — Springer Nature
Key information
Authors:
Published in
02/01/2025
Abstract
We consider the steady Navier–Stokes equations with mixed boundary conditions, where a regularized directional do-nothing (RDDN) condition is defined on the Neumann boundary portion. An auxiliary Stokes reference flow, which also works as a lifting of the inhomogeneous Dirichlet boundary values, is used to define the RDDN condition. Our aim is to study the minimization of a velocity tracking cost functional with controls localized on a part of the boundary. We prove the existence of a solution for this optimal control problem and derive the corresponding first order necessary optimality conditions in terms of dual variables. All results are obtained under appropriate assumptions on the size of the data and the controls, which, however, are less restrictive when compared with the case of the classical do-nothing outflow condition. This is further confirmed by the numerical examples presented, which include scenarios where only noisy data is available.
Publication details
Authors in the community:
Jorge Filipe Duarte Tiago
ist90590
Publisher
Springer Nature
Link to the publisher's version
https://link.springer.com/article/10.1007/s00245-024-10216-4
Title of the publication container
Applied Mathematics and Optimization
Volume
91
Issue
1
Fields of Science and Technology (FOS)
mathematics - Mathematics
Publication language (ISO code)
por - Portuguese
Rights type:
Open access
Financing entity
Fundação para a Ciência e a Tecnologia
Identifier for the funding entity: UIDB/04621/2020