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

Abstract

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.

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Funding

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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Correspondence to Bui Trong Kien.

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Kien, B.T. Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations. Acta Math Vietnam 44, 431–448 (2019). https://doi.org/10.1007/s40306-018-00304-3

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Keywords

  • 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