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Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers
1. | Université de Toulouse & CNRS, Institut de Mathématiques, UMR 5219, 31062 Toulouse Cedex 9, France, France |
[1] |
Mehdi Badra. Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control. Discrete and Continuous Dynamical Systems, 2012, 32 (4) : 1169-1208. doi: 10.3934/dcds.2012.32.1169 |
[2] |
Varga K. Kalantarov, Edriss S. Titi. Global stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1325-1345. doi: 10.3934/dcdsb.2018153 |
[3] |
Tobias Breiten, Karl Kunisch. Feedback stabilization of the three-dimensional Navier-Stokes equations using generalized Lyapunov equations. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4197-4229. doi: 10.3934/dcds.2020178 |
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Andrei Fursikov, Alexey V. Gorshkov. Certain questions of feedback stabilization for Navier-Stokes equations. Evolution Equations and Control Theory, 2012, 1 (1) : 109-140. doi: 10.3934/eect.2012.1.109 |
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Chérif Amrouche, María Ángeles Rodríguez-Bellido. On the very weak solution for the Oseen and Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 159-183. doi: 10.3934/dcdss.2010.3.159 |
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A. V. Fursikov. Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 289-314. doi: 10.3934/dcds.2004.10.289 |
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Enrique Fernández-Cara. Motivation, analysis and control of the variable density Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2012, 5 (6) : 1021-1090. doi: 10.3934/dcdss.2012.5.1021 |
[8] |
Evrad M. D. Ngom, Abdou Sène, Daniel Y. Le Roux. Global stabilization of the Navier-Stokes equations around an unstable equilibrium state with a boundary feedback controller. Evolution Equations and Control Theory, 2015, 4 (1) : 89-106. doi: 10.3934/eect.2015.4.89 |
[9] |
Evrad M. D. Ngom, Abdou Sène, Daniel Y. Le Roux. Boundary stabilization of the Navier-Stokes equations with feedback controller via a Galerkin method. Evolution Equations and Control Theory, 2014, 3 (1) : 147-166. doi: 10.3934/eect.2014.3.147 |
[10] |
Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2067-2088. doi: 10.3934/dcdsb.2017085 |
[11] |
Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control and Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029 |
[12] |
C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403 |
[13] |
Takayuki Kubo, Ranmaru Matsui. On pressure stabilization method for nonstationary Navier-Stokes equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2283-2307. doi: 10.3934/cpaa.2018109 |
[14] |
Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Mean--field control and Riccati equations. Networks and Heterogeneous Media, 2015, 10 (3) : 699-715. doi: 10.3934/nhm.2015.10.699 |
[15] |
Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations and Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495 |
[16] |
Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations and Control Theory, 2022, 11 (2) : 347-371. doi: 10.3934/eect.2020110 |
[17] |
Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D Navier-Stokes equations with mixed control-state constraints. Mathematical Control and Related Fields, 2012, 2 (1) : 61-80. doi: 10.3934/mcrf.2012.2.61 |
[18] |
Cătălin-George Lefter, Elena-Alexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 777-787. doi: 10.3934/mcrf.2018034 |
[19] |
Viorel Barbu, Ionuţ Munteanu. Internal stabilization of Navier-Stokes equation with exact controllability on spaces with finite codimension. Evolution Equations and Control Theory, 2012, 1 (1) : 1-16. doi: 10.3934/eect.2012.1.1 |
[20] |
Xue-Li Song, Yan-Ren Hou. Attractors for the three-dimensional incompressible Navier-Stokes equations with damping. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 239-252. doi: 10.3934/dcds.2011.31.239 |
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