First- and Second-Order Necessary Optimality Conditions for Optimal Control Problems Governed by Stationary Navier–Stokes Equations with Pure State Constraints

Vietnam Journal of Mathematics ◽

10.1007/s10013-015-0173-8 ◽

2015 ◽

Vol 44 (1) ◽

pp. 103-131 ◽

Author(s):

Bui Trong Kien ◽

Gue Myung Lee ◽

Nguyen Hai Son

Keyword(s):

Optimal Control ◽

State Constraints ◽

Optimal Control Problems ◽

Stokes Equations ◽

Necessary Optimality Conditions ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations ◽

Pure State Constraints ◽

Stationary Navier Stokes Equations

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

Acta Mathematica Vietnamica ◽

10.1007/s40306-018-00304-3 ◽

2018 ◽

Vol 44 (2) ◽

pp. 431-448 ◽

Author(s):

Bui Trong Kien

Keyword(s):

Optimal Control ◽

Optimality Conditions ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Solution Stability ◽

Navier Stokes Equations ◽

Second Order Optimality Conditions ◽

Stationary Navier Stokes Equations

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Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls

Mathematics of Computation ◽

10.1090/s0025-5718-1991-1079020-5 ◽

1991 ◽

Vol 57 (195) ◽

pp. 123-123 ◽

Author(s):

M. D. Gunzburger ◽

L. Hou ◽

T. P. Svobodny

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Stokes Equations ◽

Finite Element Approximation ◽

Navier Stokes ◽

Control Problems ◽

Element Approximation ◽

Navier Stokes Equations ◽

Stationary Navier Stokes Equations

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Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1991250607111 ◽

1991 ◽

Vol 25 (6) ◽

pp. 711-748 ◽

Author(s):

M. D. Gunzburger ◽

L. S. Hou ◽

Th. P. Svobodny

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Stokes Equations ◽

Finite Element Approximation ◽

Navier Stokes ◽

Control Problems ◽

Element Approximation ◽

Navier Stokes Equations ◽

Stationary Navier Stokes Equations

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A projection-based variational multiscale method for the optimal control problems governed by the stationary Navier–Stokes equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.03.005 ◽

2016 ◽

Vol 106 ◽

pp. 116-128

Author(s):

Fikriye Yılmaz ◽

Aytekin Çıbık

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Multiscale Method ◽

Navier Stokes ◽

Control Problems ◽

Variational Multiscale Method ◽

Navier Stokes Equations ◽

Variational Multiscale ◽

Stationary Navier Stokes Equations

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Second-Order Necessary Optimality Conditions for a Class of Optimal Control Problems Governed by Partial Differential Equations with Pure State Constraints

Journal of Optimization Theory and Applications ◽

10.1007/s10957-014-0628-1 ◽

2014 ◽

Vol 165 (1) ◽

pp. 30-61 ◽

Author(s):

B. T. Kien ◽

V. H. Nhu ◽

A. Rösch

Keyword(s):

Optimal Control ◽

Partial Differential Equations ◽

Differential Equations ◽

Optimality Conditions ◽

State Constraints ◽

Optimal Control Problems ◽

Necessary Optimality Conditions ◽

Control Problems ◽

Pure State Constraints

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Maximum Principle for Some Optimal Control Problems Governed by 2D Nonlocal Cahn–Hillard–Navier–Stokes Equations

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-020-00493-8 ◽

2020 ◽

Vol 22 (3) ◽

Author(s):

Tania Biswas ◽

Sheetal Dharmatti ◽

Manil T. Mohan

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations

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Analysis of the SQP-Method for Optimal Control Problems Governed by the Nonstationary Navier–Stokes Equations Based on $L^p$-theory

SIAM Journal on Control and Optimization ◽

10.1137/s0363012904443506 ◽

2007 ◽

Vol 46 (3) ◽

pp. 1133-1153 ◽

Author(s):

Daniel Wachsmuth

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations

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Differential Stability of Control-Constrained Optimal Control Problems for the Navier-Stokes Equations

Numerical Functional Analysis and Optimization ◽

10.1080/01630560500434278 ◽

2005 ◽

Vol 26 (7-8) ◽

pp. 829-850 ◽

Author(s):

Roland Griesse ◽

Michael Hintermüller ◽

Michael Hinze

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations ◽

Constrained Optimal Control ◽

Differential Stability

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Optimal control problems constrained by the stochastic Navier–Stokes equations with multiplicative Lévy noise

Mathematische Nachrichten ◽

10.1002/mana.201700185 ◽

2019 ◽

Vol 292 (7) ◽

pp. 1444-1461

Author(s):

Peter Benner ◽

Christoph Trautwein

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Lévy Noise ◽

Control Problems ◽

Navier Stokes Equations ◽

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Optimal Control Problems for the Navier-Stokes Equations

Lectures on Applied Mathematics ◽

10.1007/978-3-642-59709-1_11 ◽

2000 ◽

pp. 143-155 ◽

Author(s):

A. Fürsikov ◽

M. Gunzburger ◽

L. S. Hou ◽

S. Manservisi

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations

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