Acta Mathematica Vietnamica

, Volume 44, Issue 2, pp 431–448 | Cite as

Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations

  • Bui Trong KienEmail author


In this paper, a class of parametric optimal control problems governed by stationary Navier-Stokes equations with mixed pointwise constraints is considered. We give no-gap second-order necessary and sufficient conditions for unperturbed problem. We show that if the strictly second-order sufficient condition for unperturbed problem is valid and the objective function is locally Lipschitz continuous, then the solution map is locally upper Hölder continuous at the reference parameter.


Optimal control Stationary Navier-stokes equations Solution stability Locally upper Hölder continuity Second-order necessary optimality condition Second-order sufficient optimality condition 

Mathematics Subject Classification (2010)

49K20 35J25 


Funding Information

This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2015.13.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Optimization and Control Theory, Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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