On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions
ESAIM: COCV, 1 (1996) 35-75
Published online: 2002-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Remarks on control and inverse problems for PDEs
Emique Fernández-CaraSeMA Journal (2024)
https://doi.org/10.1007/s40324-024-00363-7
Stabilization of 2D Navier–Stokes Equations by Means of Actuators with Locally Supported Vorticity
Sérgio S. Rodrigues and Dagmawi A. SeifuJournal of Dynamical and Control Systems 30 (1) (2024)
https://doi.org/10.1007/s10883-023-09677-7
Droplet impact simulation with Cahn–Hilliard phase field method coupling Navier-slip boundary and dynamic contact angle model
Zunru Fu, Haichuan Jin, Guice Yao and Dongsheng WenPhysics of Fluids 36 (4) (2024)
https://doi.org/10.1063/5.0202604
A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations
Nikolai Chemetov and Fernanda CiprianoJournal of Optimization Theory and Applications 203 (2) 1847 (2024)
https://doi.org/10.1007/s10957-024-02416-3
Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions
Manuel Rissel and Ya-Guang WangJournal de Mathématiques Pures et Appliquées 190 103601 (2024)
https://doi.org/10.1016/j.matpur.2024.103601
Slip with friction boundary conditions for the Navier–Stokes-α turbulence model and the effects of the friction on the reattachment point
Özgül İlhanInternational Journal of Non-Linear Mechanics 159 104614 (2024)
https://doi.org/10.1016/j.ijnonlinmec.2023.104614
Quelques résultats sur la commandabilité et la stabilisation des systèmes non linéaires
Jean-Michel CoronJournées mathématiques X-UPS 127 (2024)
https://doi.org/10.5802/xups.1999-02
Contrôle et équations aux dérivées partielles
Jean-Pierre PuelJournées mathématiques X-UPS 203 (2024)
https://doi.org/10.5802/xups.1999-03
Global Controllability of the Boussinesq System with Navier-Slip-with-Friction and Robin Boundary Conditions
F. W. Chaves-Silva, E. Fernández-Cara, K. Le Balc’h, J. L. F. Machado and D. A. SouzaSIAM Journal on Control and Optimization 61 (2) 484 (2023)
https://doi.org/10.1137/21M1425566
On uniform controllability of 1D transport equations in the vanishing viscosity limit
Camille Laurent and Matthieu LéautaudComptes Rendus. Mathématique 361 (G1) 265 (2023)
https://doi.org/10.5802/crmath.405
(2023)
https://doi.org/10.2139/ssrn.4579161
Numerical Control: Part A
Francesco Ballarin, Gianluigi Rozza and Maria StrazzulloHandbook of Numerical Analysis, Numerical Control: Part A 23 307 (2022)
https://doi.org/10.1016/bs.hna.2021.12.009
A 3D Non-Stationary Boussinesq System with Navier-slip Boundary Conditions
Exequiel Mallea-Zepeda and Raul Nina-MollisacaBulletin of the Brazilian Mathematical Society, New Series 53 (4) 1331 (2022)
https://doi.org/10.1007/s00574-022-00307-7
Feedback Boundary Stabilization to Trajectories for 3D Navier–Stokes Equations
Sérgio S. RodriguesApplied Mathematics & Optimization 84 (S2) 1149 (2021)
https://doi.org/10.1007/s00245-017-9474-5
Control Problem Related to 2D Stokes Equations with Variable Density and Viscosity
Evgenii S. Baranovskii, Eber Lenes, Exequiel Mallea-Zepeda, Jonnathan Rodríguez and Lautaro VásquezSymmetry 13 (11) 2050 (2021)
https://doi.org/10.3390/sym13112050
Remote trajectory tracking of rigid bodies immersed in a two-dimensional perfect incompressible fluid
Olivier Glass, József J. Kolumbán and Franck SueurPure and Applied Analysis 3 (4) 613 (2021)
https://doi.org/10.2140/paa.2021.3.613
A Proof of Approximate Controllability of the 3D Navier--Stokes System via a Linear Test
Vahagn NersesyanSIAM Journal on Control and Optimization 59 (4) 2411 (2021)
https://doi.org/10.1137/20M1368689
Small-time global stabilization of the viscous Burgers equation with three scalar controls
Jean-Michel Coron and Shengquan XiangJournal de Mathématiques Pures et Appliquées 151 212 (2021)
https://doi.org/10.1016/j.matpur.2021.03.001
On uniform observability of gradient flows in the vanishing viscosity limit
Camille Laurent and Matthieu LéautaudJournal de l’École polytechnique — Mathématiques 8 439 (2021)
https://doi.org/10.5802/jep.151
A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions
Cristian Duarte-Leiva, Sebastián Lorca and Exequiel Mallea-ZepedaSymmetry 13 (8) 1348 (2021)
https://doi.org/10.3390/sym13081348
Control at a distance of the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid
József J. KolumbánJournal of Differential Equations 269 (1) 764 (2020)
https://doi.org/10.1016/j.jde.2019.12.021
Uniform Controllability of a Stokes Problem with a Transport Term in the Zero-Diffusion Limit
Jon Asier Bárcena-PetiscoSIAM Journal on Control and Optimization 58 (3) 1597 (2020)
https://doi.org/10.1137/19M1252004
Some control problems for the Burgers equation
Peng GaoRocky Mountain Journal of Mathematics 50 (2) (2020)
https://doi.org/10.1216/rmj.2020.50.559
External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid
Olivier Glass, József J. Kolumbán and Franck SueurAnalysis & PDE 13 (3) 651 (2020)
https://doi.org/10.2140/apde.2020.13.651
Recent Advances in Pure and Applied Mathematics
Enrique Fernández-CaraRSME Springer Series, Recent Advances in Pure and Applied Mathematics 4 1 (2020)
https://doi.org/10.1007/978-3-030-41321-7_1
An Approximating Control Design for Optimal Mixing by Stokes Flows
Weiwei HuApplied Mathematics & Optimization 82 (2) 471 (2020)
https://doi.org/10.1007/s00245-018-9535-4
Local Exact Boundary Controllability for the Compressible Navier--Stokes Equations
Nicolás MolinaSIAM Journal on Control and Optimization 57 (3) 2152 (2019)
https://doi.org/10.1137/17M1127648
Singular Perturbations and Boundary Layers
Gung-Min Gie, Makram Hamouda, Chang-Yeol Jung and Roger M. TemamApplied Mathematical Sciences, Singular Perturbations and Boundary Layers 200 307 (2018)
https://doi.org/10.1007/978-3-030-00638-9_7
Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations
Sylvain Ervedoza and Marc SavelESAIM: Control, Optimisation and Calculus of Variations 24 (1) 211 (2018)
https://doi.org/10.1051/cocv/2017008
Boundary Control for Optimal Mixing by Stokes Flows
Weiwei HuApplied Mathematics & Optimization 78 (1) 201 (2018)
https://doi.org/10.1007/s00245-017-9404-6
Local null controllability of the N-dimensional Navier–Stokes system with nonlinear Navier-slip boundary conditions and N − 1 scalar controls
Sergio Guerrero and Cristhian MontoyaJournal de Mathématiques Pures et Appliquées 113 37 (2018)
https://doi.org/10.1016/j.matpur.2018.03.004
Boundary Control for Optimal Mixing via Navier--Stokes Flows
Weiwei Hu and Jiahong WuSIAM Journal on Control and Optimization 56 (4) 2768 (2018)
https://doi.org/10.1137/17M1148049
Remarks concerning the approximate controllability of the 3D Navier–Stokes and Boussinesq systems
Enrique Fernández-Cara, Ivaldo T. De Sousa and Franciane B. VieraSeMA Journal 74 (3) 237 (2017)
https://doi.org/10.1007/s40324-017-0111-7
PREFACE
Karine Beauchard and Emmanuel TrélatESAIM: Control, Optimisation and Calculus of Variations 22 (4) 913 (2016)
https://doi.org/10.1051/cocv/2016057
Lagrangian Controllability of the 1-Dimensional Korteweg--de Vries Equation
Ludovick GagnonSIAM Journal on Control and Optimization 54 (6) 3152 (2016)
https://doi.org/10.1137/140964783
On the convergence of the two-dimensional second grade fluid model to the Navier–Stokes equation
Nadir AradaJournal of Differential Equations 260 (3) 2557 (2016)
https://doi.org/10.1016/j.jde.2015.10.019
Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations
Mehdi Badra, Sylvain Ervedoza and Sergio GuerreroAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 33 (2) 529 (2016)
https://doi.org/10.1016/j.anihpc.2014.11.006
On the controllability of the relativistic Vlasov–Maxwell system
Olivier Glass and Daniel Han-KwanJournal de Mathématiques Pures et Appliquées 103 (3) 695 (2015)
https://doi.org/10.1016/j.matpur.2014.07.007
Null controllability of the linearized compressible Navier–Stokes equations using moment method
Shirshendu Chowdhury and Debanjana MitraJournal of Evolution Equations 15 (2) 331 (2015)
https://doi.org/10.1007/s00028-014-0263-1
Approximate controllability for linearized compressible barotropic Navier–Stokes system in one and two dimensions
Shirshendu ChowdhuryJournal of Mathematical Analysis and Applications 422 (2) 1034 (2015)
https://doi.org/10.1016/j.jmaa.2014.09.011
Theoretical and Numerical Local Null Controllability of a Ladyzhenskaya–Smagorinsky Model of Turbulence
E. Fernández-Cara, J. Límaco and S. B. de MenezesJournal of Mathematical Fluid Mechanics 17 (4) 669 (2015)
https://doi.org/10.1007/s00021-015-0232-7
Uniform local null control of the Leray-αmodel
Fágner D. Araruna, Enrique Fernández-Cara and Diego A. SouzaESAIM: Control, Optimisation and Calculus of Variations 20 (4) 1181 (2014)
https://doi.org/10.1051/cocv/2014011
Geometric Control Theory and Sub-Riemannian Geometry
Andrei A. AgrachevSpringer INdAM Series, Geometric Control Theory and Sub-Riemannian Geometry 5 1 (2014)
https://doi.org/10.1007/978-3-319-02132-4_1
Small time global null controllability for a viscous Burgers' equation despite the presence of a boundary layer
Frédéric MarbachJournal de Mathématiques Pures et Appliquées 102 (2) 364 (2014)
https://doi.org/10.1016/j.matpur.2013.11.013
On the “viscous incompressible fluid + rigid body” system with Navier conditions
Gabriela Planas and Franck SueurAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 31 (1) 55 (2014)
https://doi.org/10.1016/j.anihpc.2013.01.004
Local null controllability of the three-dimensional Navier–Stokes system with a distributed control having two vanishing components
Jean-Michel Coron and Pierre LissyInventiones mathematicae 198 (3) 833 (2014)
https://doi.org/10.1007/s00222-014-0512-5
Simultaneous local exact controllability of 1D bilinear Schrödinger equations
Morgan MoranceyAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 31 (3) 501 (2014)
https://doi.org/10.1016/j.anihpc.2013.05.001
Optimization with PDE Constraints
Jean-Pierre PuelLecture Notes in Computational Science and Engineering, Optimization with PDE Constraints 101 379 (2014)
https://doi.org/10.1007/978-3-319-08025-3_12
Stabilization of the 2D incompressible Euler system in an infinite strip
Hayk NersisyanAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 30 (4) 737 (2013)
https://doi.org/10.1016/j.anihpc.2012.12.002
Motivation, analysis and control of the variable density Navier-Stokes equations
Enrique Fernández-CaraDiscrete & Continuous Dynamical Systems - S 5 (6) 1021 (2012)
https://doi.org/10.3934/dcdss.2012.5.1021
Boundary layer analysis of the Navier–Stokes equations with generalized Navier boundary conditions
Gung-Min Gie and James P. KelliherJournal of Differential Equations 253 (6) 1862 (2012)
https://doi.org/10.1016/j.jde.2012.06.008
A result concerning the global approximate controllability of the Navier–Stokes system in dimension 3
Sergio Guerrero, O.Yu. Imanuvilov and J.-P. PuelJournal de Mathématiques Pures et Appliquées 98 (6) 689 (2012)
https://doi.org/10.1016/j.matpur.2012.05.008
On the control of viscoelastic Jeffreys fluids
A. Doubova and E. Fernández-CaraSystems & Control Letters 61 (4) 573 (2012)
https://doi.org/10.1016/j.sysconle.2012.02.003
Local Exact Controllability for the One-Dimensional Compressible Navier–Stokes Equation
Sylvain Ervedoza, Olivier Glass, Sergio Guerrero and Jean-Pierre PuelArchive for Rational Mechanics and Analysis 206 (1) 189 (2012)
https://doi.org/10.1007/s00205-012-0534-3
Some Controllability Results for Linear Viscoelastic Fluids
J.L. Boldrini, A. Doubova, E. Fernández-Cara and M. González-BurgosSIAM Journal on Control and Optimization 50 (2) 900 (2012)
https://doi.org/10.1137/100813592
Uniform Controllability of Scalar Conservation Laws in the Vanishing Viscosity Limit
Matthieu LéautaudSIAM Journal on Control and Optimization 50 (3) 1661 (2012)
https://doi.org/10.1137/100803043
Existence of global strong solutions for the Saint-Venant system with large initial data on the irrotational part of the velocity
Boris HaspotComptes Rendus. Mathématique 350 (5-6) 249 (2012)
https://doi.org/10.1016/j.crma.2012.03.007
Mathematics of Complexity and Dynamical Systems
Olivier GlassMathematics of Complexity and Dynamical Systems 755 (2012)
https://doi.org/10.1007/978-1-4614-1806-1_46
Control of Partial Differential Equations
Olivier GlassLecture Notes in Mathematics, Control of Partial Differential Equations 2048 131 (2012)
https://doi.org/10.1007/978-3-642-27893-8_3
Recent results on the controllability of linear coupled parabolic problems: A survey
Farid Ammar-Khodja, Assia Benabdallah, Manuel González-Burgos and Luz de TeresaMathematical Control & Related Fields 1 (3) 267 (2011)
https://doi.org/10.3934/mcrf.2011.1.267
Applied and Numerical Partial Differential Equations
Enrique Fernández-CaraComputational Methods in Applied Sciences, Applied and Numerical Partial Differential Equations 15 81 (2010)
https://doi.org/10.1007/978-90-481-3239-3_7
4804 (2009)
https://doi.org/10.1007/978-0-387-30440-3_284
On the global null controllability of a Navier–Stokes system with Navier slip boundary conditions
Marianne ChapoulyJournal of Differential Equations 247 (7) 2094 (2009)
https://doi.org/10.1016/j.jde.2009.06.022
Local null controllability of the two-dimensional Navier–Stokes system in the torus with a control force having a vanishing component
Jean-Michel Coron and Sergio GuerreroJournal de Mathématiques Pures et Appliquées 92 (5) 528 (2009)
https://doi.org/10.1016/j.matpur.2009.05.015
Exact controllability of Galerkin’s approximations of micropolar fluids
F. Araruna, F. Chaves-Silva and M. Rojas-MedarProceedings of the American Mathematical Society 138 (4) 1361 (2009)
https://doi.org/10.1090/S0002-9939-09-10154-5
GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION
MARIANNE CHAPOULYCommunications in Contemporary Mathematics 11 (03) 495 (2009)
https://doi.org/10.1142/S0219199709003454
Feedback stabilization of 2D Navier–Stokes equations with Navier slip boundary conditions
Cătălin LefterNonlinear Analysis: Theory, Methods & Applications 70 (1) 553 (2009)
https://doi.org/10.1016/j.na.2007.12.026
Optimal and Robust Control of Fluid Flows: Some Theoretical and Computational Aspects
T. Tachim Medjo, R. Temam and M. ZianeApplied Mechanics Reviews 61 (1) (2008)
https://doi.org/10.1115/1.2830523
Local exact Lagrangian controllability of the Burgers viscous equation
Thierry HorsinAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 25 (2) 219 (2008)
https://doi.org/10.1016/j.anihpc.2006.11.009
Steady solutions of the Navier–Stokes equations with threshold slip boundary conditions
C. Le Roux and A. TaniMathematical Methods in the Applied Sciences 30 (5) 595 (2007)
https://doi.org/10.1002/mma.802
Null controllability of the Burgers system with distributed controls
Enrique Fernández-Cara and Sergio GuerreroSystems & Control Letters 56 (5) 366 (2007)
https://doi.org/10.1016/j.sysconle.2006.10.022
A Closed-Form Feedback Controller for Stabilization of the Linearized 2-D Navier–Stokes Poiseuille System
Rafael Vazquez and Miroslav KrsticIEEE Transactions on Automatic Control 52 (12) 2298 (2007)
https://doi.org/10.1109/TAC.2007.910686
Exact controllability in projections for three-dimensional Navier–Stokes equations
Armen ShirikyanAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 24 (4) 521 (2007)
https://doi.org/10.1016/j.anihpc.2006.04.002
Remarks on global controllability for the Burgers equation with two control forces
S. Guerrero and O.Yu. ImanuvilovAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 24 (6) 897 (2007)
https://doi.org/10.1016/j.anihpc.2006.06.010
Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations
J.-P. RaymondJournal de Mathématiques Pures et Appliquées 87 (6) 627 (2007)
https://doi.org/10.1016/j.matpur.2007.04.002
Handbook of Differential Equations: Evolutionary Equations
Enrique ZuazuaHandbook of Differential Equations: Evolutionary Equations 3 527 (2007)
https://doi.org/10.1016/S1874-5717(07)80010-7
Control of Fluid Flow
Andras Balogh and Miroslav KrsticLecture Notes in Control and Information Sciences, Control of Fluid Flow 330 157 (2006)
https://doi.org/10.1007/978-3-540-36085-8_7
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
Sergio GuerreroESAIM: Control, Optimisation and Calculus of Variations 12 (3) 484 (2006)
https://doi.org/10.1051/cocv:2006006
Approximate Controllability of Three-Dimensional Navier–Stokes Equations
Armen ShirikyanCommunications in Mathematical Physics 266 (1) 123 (2006)
https://doi.org/10.1007/s00220-006-0007-3
Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions
Sergio Guerrero, Oleg Yurievich Imanuvilov and Jean-Pierre PuelComptes Rendus. Mathématique 343 (9) 573 (2006)
https://doi.org/10.1016/j.crma.2006.09.023
Some Controllability Results forthe N-Dimensional Navier--Stokes and Boussinesq systems with N-1 scalar controls
Enrique Fernández-Cara, Sergio Guerrero, Oleg Yu. Imanuvilov and Jean-Pierre PuelSIAM Journal on Control and Optimization 45 (1) 146 (2006)
https://doi.org/10.1137/04061965X
5329 (2006)
https://doi.org/10.1109/CDC.2006.377593
Time‐dependent flow across a step: the slip with friction boundary condition
Volker John and Anastasios LiakosInternational Journal for Numerical Methods in Fluids 50 (6) 713 (2006)
https://doi.org/10.1002/fld.1074
Controllability of a quantum particle in a moving potential well
Karine Beauchard and Jean-Michel CoronJournal of Functional Analysis 232 (2) 328 (2006)
https://doi.org/10.1016/j.jfa.2005.03.021
Mechanics, Dynamics, and Control of a Single-Input Aquatic Vehicle With Variable Coefficient of Lift
Scott D. Kelly and Ramadev B. HukkeriIEEE Transactions on Robotics 22 (6) 1254 (2006)
https://doi.org/10.1109/TRO.2006.882934
Global Carleman Inequalities for Parabolic Systems and Applications to Controllability
Enrique Fernández‐Cara and Sergio GuerreroSIAM Journal on Control and Optimization 45 (4) 1395 (2006)
https://doi.org/10.1137/S0363012904439696
7358 (2005)
https://doi.org/10.1109/CDC.2005.1583349
On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well
Jean-Michel CoronComptes Rendus. Mathématique 342 (2) 103 (2005)
https://doi.org/10.1016/j.crma.2005.11.004
STEADY STOKES FLOWS WITH THRESHOLD SLIP BOUNDARY CONDITIONS
C. LE ROUXMathematical Models and Methods in Applied Sciences 15 (08) 1141 (2005)
https://doi.org/10.1142/S0218202505000686
Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
Enrique ZuazuaSIAM Review 47 (2) 197 (2005)
https://doi.org/10.1137/S0036144503432862
Solving inverse problems involving the Navier–Stokes equations discretized by a Lagrange–Galerkin method
Gilles Fourestey and Marwan MoubachirComputer Methods in Applied Mechanics and Engineering 194 (6-8) 877 (2005)
https://doi.org/10.1016/j.cma.2004.07.006
Local exact controllability of the Navier–Stokes system
E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov and J.-P. PuelJournal de Mathématiques Pures et Appliquées 83 (12) 1501 (2004)
https://doi.org/10.1016/j.matpur.2004.02.010
A Noise Control Problem Arising in a Flow Duct
Jocelyne Vétillard and Philippe DestuynderSIAM Journal on Applied Mathematics 64 (6) 1987 (2004)
https://doi.org/10.1137/S0036139902418912
Feedback stabilization of Navier–Stokes equations
Viorel BarbuESAIM: Control, Optimisation and Calculus of Variations 9 197 (2003)
https://doi.org/10.1051/cocv:2003009
On the controllability of the Vlasov–Poisson system
Olivier GlassJournal of Differential Equations 195 (2) 332 (2003)
https://doi.org/10.1016/S0022-0396(03)00066-4
The second grade fluid and averaged Euler equations with Navier-slip boundary conditions
Adriana Valentina Busuioc and Tudor S RatiuNonlinearity 16 (3) 1119 (2003)
https://doi.org/10.1088/0951-7715/16/3/318
Jean Leray ’99 Conference Proceedings
J. L. LionsJean Leray ’99 Conference Proceedings 543 (2003)
https://doi.org/10.1007/978-94-017-2008-3_33
Controllability of a fluid in a 1-D tank
Jean-Michel CoronIFAC Proceedings Volumes 36 (19) 11 (2003)
https://doi.org/10.1016/S1474-6670(17)33295-0
Local internal controllability of the Boussinesq system
Lijuan Wang and Gengsheng WangNonlinear Analysis: Theory, Methods & Applications 53 (5) 637 (2003)
https://doi.org/10.1016/S0362-546X(02)00173-6
Аппроксимативная управляемость системы Навье - Стокса в неограниченных областях
Pavel Olegovich Shorygin and Павел Олегович ШорыгинМатематический сборник 194 (11) 141 (2003)
https://doi.org/10.4213/sm784