ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

Insensitizing controls with one vanishing component for the Navier–Stokes system

N. Carreño and M. Gueye
Journal de Mathématiques Pures et Appliquées 101 (1) 27 (2014)
DOI: 10.1016/j.matpur.2013.03.007
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Equivalence of three different kinds of optimal control problems for Stokes equations

Peijie HE and Qishu YAN
Acta Mathematica Scientia 35 (3) 709 (2015)
DOI: 10.1016/S0252-9602(15)30016-3
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Applied and Numerical Partial Differential Equations

Enrique Fernández-Cara
Computational Methods in Applied Sciences, Applied and Numerical Partial Differential Equations 15 81 (2010)
DOI: 10.1007/978-90-481-3239-3_7
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Optimization with PDE Constraints

Jean-Pierre Puel
Lecture Notes in Computational Science and Engineering, Optimization with PDE Constraints 101 379 (2014)
DOI: 10.1007/978-3-319-08025-3_12
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On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

Jérôme Le Rousseau and Gilles Lebeau
ESAIM: Control, Optimisation and Calculus of Variations 18 (3) 712 (2012)
DOI: 10.1051/cocv/2011168
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Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations

Sylvain Ervedoza and Marc Savel
ESAIM: Control, Optimisation and Calculus of Variations 24 (1) 211 (2018)
DOI: 10.1051/cocv/2017008
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Single input controllability of a simplified fluid-structure interaction model

Yuning Liu, Takéo Takahashi and Marius Tucsnak
ESAIM: Control, Optimisation and Calculus of Variations 19 (1) 20 (2013)
DOI: 10.1051/cocv/2011196
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Une approche non classique d'un problème d'assimilation de données

Jean-Pierre Puel
Comptes Rendus Mathematique 335 (2) 161 (2002)
DOI: 10.1016/S1631-073X(02)02390-7
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Controllability of the 3D Compressible Euler System

Hayk Nersisyan
Communications in Partial Differential Equations 36 (9) 1544 (2011)
DOI: 10.1080/03605302.2011.596605
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Two-dimensional local null controllability of a rigid structure in a Navier–Stokes fluid

Muriel Boulakia and Axel Osses
Comptes Rendus Mathematique 343 (2) 105 (2006)
DOI: 10.1016/j.crma.2006.05.004
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Local Exact Controllability to the Trajectories of the Cahn–Hilliard Equation

Patricio Guzmán
Applied Mathematics & Optimization 82 (1) 279 (2020)
DOI: 10.1007/s00245-018-9500-2
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The sub-Cauchy–Stokes problem: Solvability issues and Lagrange multiplier methods with artificial boundary conditions

Elyes Ahmed and Amel Ben Abda
Journal of Computational and Applied Mathematics 338 258 (2018)
DOI: 10.1016/j.cam.2018.01.034
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Exact controllability of Galerkin’s approximations of micropolar fluids

F. Araruna, F. Chaves-Silva and M. Rojas-Medar
Proceedings of the American Mathematical Society 138 (4) 1361 (2009)
DOI: 10.1090/S0002-9939-09-10154-5
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Local Exact Controllability of Two-Phase Field Solidification Systems with Few Controls

F. D. Araruna, B. M. R. Calsavara and E. Fernández-Cara
Applied Mathematics & Optimization 78 (2) 267 (2018)
DOI: 10.1007/s00245-017-9406-4
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On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems

Mehdi Badra and Takéo Takahashi
ESAIM: Control, Optimisation and Calculus of Variations 20 (3) 924 (2014)
DOI: 10.1051/cocv/2014002
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SemiGlobal Exact Controllability of Nonlinear Plates

Matthias Eller and Daniel Toundykov
SIAM Journal on Control and Optimization 53 (4) 2480 (2015)
DOI: 10.1137/130939705
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Stabilization of Parabolic Nonlinear Systems with Finite Dimensional Feedback or Dynamical Controllers: Application to the Navier–Stokes System

Mehdi Badra and Takéo Takahashi
SIAM Journal on Control and Optimization 49 (2) 420 (2011)
DOI: 10.1137/090778146
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Internal stabilizability of the Navier–Stokes equations

Viorel Barbu and Cătălin Lefter
Systems & Control Letters 48 (3-4) 161 (2003)
DOI: 10.1016/S0167-6911(02)00261-X
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On the control of viscoelastic Jeffreys fluids

A. Doubova and E. Fernández-Cara
Systems & Control Letters 61 (4) 573 (2012)
DOI: 10.1016/j.sysconle.2012.02.003
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Exact Controllability of Galerkin's Approximations for the Oldroyd Fluid System

A. O. Marinho, A. T. Lourêdo and M. Milla Miranda
International Journal of Modeling and Optimization 4 (2) 126 (2014)
DOI: 10.7763/IJMO.2014.V4.359
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Inverse source problem for linearized Navier–Stokes equations with data in arbitrary sub-domain

Mourad Choulli, Oleg Yu. Imanuvilov, Jean-Pierre Puel and Masahiro Yamamoto
Applicable Analysis 92 (10) 2127 (2013)
DOI: 10.1080/00036811.2012.718334
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Exact internal controllability for the two-dimensional Navier–Stokes equations with the Navier slip boundary conditions

Teodor Havârneanu, Cătălin Popa and S.S. Sritharan
Systems & Control Letters 55 (12) 1022 (2006)
DOI: 10.1016/j.sysconle.2006.06.015
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Stabilization of the Boussinesq equation via internal feedback controls

Gengsheng Wang
Nonlinear Analysis: Theory, Methods & Applications 52 (2) 485 (2003)
DOI: 10.1016/S0362-546X(02)00114-1
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Exact controllability of nonlinear diffusion equations arising in reactor dynamics

K. Sakthivel, K. Balachandran and S.S. Sritharan
Nonlinear Analysis: Real World Applications 9 (5) 2029 (2008)
DOI: 10.1016/j.nonrwa.2007.06.013
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Local exact controllability of the Navier–Stokes system

E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov and J.-P. Puel
Journal de Mathématiques Pures et Appliquées 83 (12) 1501 (2004)
DOI: 10.1016/j.matpur.2004.02.010
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Insensitizing controls for a large-scale ocean circulation model

Enrique Fernández-Cara, Galina C. Garcia and Axel Osses
Comptes Rendus Mathematique 337 (4) 265 (2003)
DOI: 10.1016/S1631-073X(03)00334-0
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On the controllability of the N-dimensional Navier–Stokes and Boussinesq systems with scalar controls

Enrique Fernández-Cara, Sergio Guerrero, Oleg Yurievich Imanuvilov and Jean-Pierre Puel
Comptes Rendus Mathematique 340 (4) 275 (2005)
DOI: 10.1016/j.crma.2004.12.013
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A Nonstandard Approach to a Data Assimilation Problem and Tychonov Regularization Revisited

Jean-Pierre Puel
SIAM Journal on Control and Optimization 48 (2) 1089 (2009)
DOI: 10.1137/060670961
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Carleman Estimates for a Class of Degenerate Parabolic Operators

P. Cannarsa, P. Martinez and J. Vancostenoble
SIAM Journal on Control and Optimization 47 (1) 1 (2008)
DOI: 10.1137/04062062X
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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 Puel
SIAM Journal on Control and Optimization 45 (1) 146 (2006)
DOI: 10.1137/04061965X
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Exact Internal Controllability for the Two-Dimensional Magnetohydrodynamic Equations

Teodor Havârneanu, Cătălin Popa and S. S. Sritharan
SIAM Journal on Control and Optimization 46 (5) 1802 (2007)
DOI: 10.1137/040611884
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Local Controllability to Trajectories of the Magnetohydrodynamic Equations

Mehdi Badra
Journal of Mathematical Fluid Mechanics 16 (4) 631 (2014)
DOI: 10.1007/s00021-014-0186-1
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Local exact controllability for the two- and three-dimensional compressible Navier–Stokes equations

Sylvain Ervedoza, Olivier Glass and Sergio Guerrero
Communications in Partial Differential Equations 41 (11) 1660 (2016)
DOI: 10.1080/03605302.2016.1214597
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Local Exact Controllability of the Navier–Stokes Equations with the Condition on the Pressure on Parts of the Boundary

Tujin Kim and Daomin Cao
SIAM Journal on Control and Optimization 48 (6) 3805 (2010)
DOI: 10.1137/060650143
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Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier–Stokes Equations

Viorel Barbu, Sérgio S. Rodrigues and Armen Shirikyan
SIAM Journal on Control and Optimization 49 (4) 1454 (2011)
DOI: 10.1137/100785739
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Stackelberg–Nash null controllability for some linear and semilinear degenerate parabolic equations

F. D. Araruna, B. S. V. Araújo and E. Fernández-Cara
Mathematics of Control, Signals, and Systems 30 (3) (2018)
DOI: 10.1007/s00498-018-0220-6
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Feedback stabilization of Navier–Stokes equations

Viorel Barbu
ESAIM: Control, Optimisation and Calculus of Variations 9 197 (2003)
DOI: 10.1051/cocv:2003009
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Controllability of systems of Stokes equations with one control force: existence of insensitizing controls

Sergio Guerrero
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 24 (6) 1029 (2007)
DOI: 10.1016/j.anihpc.2006.11.001
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Global Carleman Inequalities for Parabolic Systems and Applications to Controllability

Enrique Fernández‐Cara and Sergio Guerrero
SIAM Journal on Control and Optimization 45 (4) 1395 (2006)
DOI: 10.1137/S0363012904439696
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SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION

ANNA DOUBOVA and ENRIQUE FERNÁNDEZ-CARA
Mathematical Models and Methods in Applied Sciences 15 (05) 783 (2005)
DOI: 10.1142/S0218202505000522
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On a Unique Continuation Property Related to the Boundary Stabilization of Magnetohydrodynamic Equations

Cătălin-George Lefter
Annals of the Alexandru Ioan Cuza University - Mathematics 56 (1) 1 (2010)
DOI: 10.2478/v10157-010-0001-0
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Insensitizing controls for the Navier–Stokes equations

Mamadou Gueye
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 30 (5) 825 (2013)
DOI: 10.1016/j.anihpc.2012.09.005
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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 Guerrero
Journal de Mathématiques Pures et Appliquées 92 (5) 528 (2009)
DOI: 10.1016/j.matpur.2009.05.015
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On the global null controllability of a Navier–Stokes system with Navier slip boundary conditions

Marianne Chapouly
Journal of Differential Equations 247 (7) 2094 (2009)
DOI: 10.1016/j.jde.2009.06.022
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On the control of some coupled systems of the Boussinesq kind with few controls

Diego A. Souza and Enrique Fernández-Cara
Mathematical Control and Related Fields 2 (2) 121 (2012)
DOI: 10.3934/mcrf.2012.2.121
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Local null controllability of a two-dimensional fluid-structure interaction problem

Muriel Boulakia and Axel Osses
ESAIM: Control, Optimisation and Calculus of Variations 14 (1) 1 (2008)
DOI: 10.1051/cocv:2007031
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Uniform local null control of the Leray-αmodel

Fágner D. Araruna, Enrique Fernández-Cara and Diego A. Souza
ESAIM: Control, Optimisation and Calculus of Variations 20 (4) 1181 (2014)
DOI: 10.1051/cocv/2014011
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Motivation, analysis and control of the variable density Navier-Stokes equations

Enrique Fernández-Cara
Discrete and Continuous Dynamical Systems - Series S 5 (6) 1021 (2012)
DOI: 10.3934/dcdss.2012.5.1021
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Remarks on exact controllability for Stokes and Navier–Stokes systems

Enrique Fernández-Cara, Sergio Guerrero, Oleg Yurievich Imanuvilov and Jean-Pierre Puel
Comptes Rendus Mathematique 338 (5) 375 (2004)
DOI: 10.1016/j.crma.2003.12.016
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Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system

N. Carreño, S. Guerrero and M. Gueye
ESAIM: Control, Optimisation and Calculus of Variations 21 (1) 73 (2015)
DOI: 10.1051/cocv/2014020
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Boundary observability inequalities for the 3D Oseen–Stokes system and applications

Sérgio S. Rodrigues
ESAIM: Control, Optimisation and Calculus of Variations 21 (3) 723 (2015)
DOI: 10.1051/cocv/2014045
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Local exact boundary controllability of 3D Navier–Stokes equations

Sérgio S. Rodrigues
Nonlinear Analysis: Theory, Methods & Applications 95 175 (2014)
DOI: 10.1016/j.na.2013.09.003
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On the Numerical Controllability of the Two-Dimensional Heat, Stokes and Navier–Stokes Equations

Enrique Fernández-Cara, Arnaud Münch and Diego A. Souza
Journal of Scientific Computing 70 (2) 819 (2017)
DOI: 10.1007/s10915-016-0266-x
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A result concerning the global approximate controllability of the Navier–Stokes system in dimension 3

Sergio Guerrero, O.Yu. Imanuvilov and J.-P. Puel
Journal de Mathématiques Pures et Appliquées 98 (6) 689 (2012)
DOI: 10.1016/j.matpur.2012.05.008
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A least-squares formulation for the approximation of controls for the Stokes system

Arnaud Münch
Mathematics of Control, Signals, and Systems 27 (1) 49 (2015)
DOI: 10.1007/s00498-014-0134-x
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Remarks concerning the approximate controllability of the 3D Navier–Stokes and Boussinesq systems

Enrique Fernández-Cara, Ivaldo T. De Sousa and Franciane B. Viera
SeMA Journal 74 (3) 237 (2017)
DOI: 10.1007/s40324-017-0111-7
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Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems

Oleg Yu. Imanuvilov and Jean-Pierre Puel
Comptes Rendus Mathematique 335 (1) 33 (2002)
DOI: 10.1016/S1631-073X(02)02389-0
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Local controllability of the $N$-dimensional Boussinesq system with $N-1$ scalar controls in an arbitrary control domain

Nicolás Carreño
Mathematical Control and Related Fields 2 (4) 361 (2012)
DOI: 10.3934/mcrf.2012.2.361
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Null controllability of the linearized compressible Navier–Stokes equations using moment method

Shirshendu Chowdhury and Debanjana Mitra
Journal of Evolution Equations 15 (2) 331 (2015)
DOI: 10.1007/s00028-014-0263-1
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Feedback Stabilization of Magnetohydrodynamic Equations

Cătălin-George Lefter
SIAM Journal on Control and Optimization 49 (3) 963 (2011)
DOI: 10.1137/070697124
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Stackelberg–Nash exact controllability for linear and semilinear parabolic equations

F.D. Araruna, E. Fernández-Cara and M.C. Santos
ESAIM: Control, Optimisation and Calculus of Variations 21 (3) 835 (2015)
DOI: 10.1051/cocv/2014052
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Solving inverse problems involving the Navier–Stokes equations discretized by a Lagrange–Galerkin method

Gilles Fourestey and Marwan Moubachir
Computer Methods in Applied Mechanics and Engineering 194 (6-8) 877 (2005)
DOI: 10.1016/j.cma.2004.07.006
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Local Null Controllability of the N-Dimensional Navier–Stokes System with N − 1 Scalar Controls in an Arbitrary Control Domain

N. Carreño and S. Guerrero
Journal of Mathematical Fluid Mechanics 15 (1) 139 (2013)
DOI: 10.1007/s00021-012-0093-2
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Carleman estimates for parabolic equations and applications

Masahiro Yamamoto
Inverse Problems 25 (12) 123013 (2009)
DOI: 10.1088/0266-5611/25/12/123013
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Global Carleman inequalities for Stokes and penalized Stokes equations

Mehdi Badra
Mathematical Control and Related Fields 1 (2) 149 (2011)
DOI: 10.3934/mcrf.2011.1.149
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Boundary stabilization of vibration of nonlocal micropolar elastic media

Ali Najafi, Mohammad Eghtesad and Farhang Daneshmand
Applied Mathematical Modelling 36 (8) 3447 (2012)
DOI: 10.1016/j.apm.2011.09.091
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Theoretical and numerical local null controllability for a parabolic system with local and nonlocal nonlinearities

H.R. Clark, E. Fernández-Cara, J. Limaco and L.A. Medeiros
Applied Mathematics and Computation 223 483 (2013)
DOI: 10.1016/j.amc.2013.08.035
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Local exact controllability to the trajectories of the Boussinesq system

S. Guerrero
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 23 (1) 29 (2006)
DOI: 10.1016/j.anihpc.2005.01.002
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Local Exact Controllability for the One-Dimensional Compressible Navier–Stokes Equation

Sylvain Ervedoza, Olivier Glass, Sergio Guerrero and Jean-Pierre Puel
Archive for Rational Mechanics and Analysis 206 (1) 189 (2012)
DOI: 10.1007/s00205-012-0534-3
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Spectral inequality and optimal cost of controllability for the Stokes system

Felipe W. Chaves-Silva and Gilles Lebeau
ESAIM: Control, Optimisation and Calculus of Variations 22 (4) 1137 (2016)
DOI: 10.1051/cocv/2016034
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Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero
ESAIM: Control, Optimisation and Calculus of Variations 12 (3) 484 (2006)
DOI: 10.1051/cocv:2006006
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Exact controllability for the magnetohydrodynamic equations

Viorel Barbu, Teodor Havârneanu, Cătălin Popa and S. S. Sritharan
Communications on Pure and Applied Mathematics 56 (6) 732 (2003)
DOI: 10.1002/cpa.10072
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Controls Insensitizing the Observation of a Quasi-geostrophic Ocean Model

Enrique Fernández-Cara, Galina C. Garcia and Axel Osses
SIAM Journal on Control and Optimization 43 (5) 1616 (2005)
DOI: 10.1137/S0363012903433607
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Local exact Lagrangian controllability of the Burgers viscous equation

Thierry Horsin
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 25 (2) 219 (2008)
DOI: 10.1016/j.anihpc.2006.11.009
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Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations

Mehdi Badra, Sylvain Ervedoza and Sergio Guerrero
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 33 (2) 529 (2016)
DOI: 10.1016/j.anihpc.2014.11.006
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Controllability of the Navier–Stokes Equation in a Rectangle with a Little Help of a Distributed Phantom Force

Jean-Michel Coron, Frédéric Marbach, Franck Sueur and Ping Zhang
Annals of PDE 5 (2) (2019)
DOI: 10.1007/s40818-019-0073-4
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Theoretical and numerical local null controllability of a quasi-linear parabolic equation in dimensions 2 and 3

E. Fernández-Cara, J. Límaco and I. Marín-Gayte
Journal of the Franklin Institute 358 (5) 2846 (2021)
DOI: 10.1016/j.jfranklin.2021.01.031
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Optimal and Robust Control of Fluid Flows: Some Theoretical and Computational Aspects

T. Tachim Medjo, R. Temam and M. Ziane
Applied Mechanics Reviews 61 (1) 010802 (2008)
DOI: 10.1115/1.2830523
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Approximate controllability for linearized compressible barotropic Navier–Stokes system in one and two dimensions

Shirshendu Chowdhury
Journal of Mathematical Analysis and Applications 422 (2) 1034 (2015)
DOI: 10.1016/j.jmaa.2014.09.011
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Switching Controls for Analytic Semigroups and Applications to Parabolic Systems

Felipe Wallison Chaves-Silva, Sylvain Ervedoza and Diego A. Souza
SIAM Journal on Control and Optimization 59 (4) 2820 (2021)
DOI: 10.1137/20M1356920
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Control of Fluid Flow

Claude Bardos
Lecture Notes in Control and Information Sciences, Control of Fluid Flow 330 139 (2006)
DOI: 10.1007/978-3-540-36085-8_6
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Mathematics of Complexity and Dynamical Systems

Olivier Glass
Mathematics of Complexity and Dynamical Systems 755 (2012)
DOI: 10.1007/978-1-4614-1806-1_46
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Control of Partial Differential Equations

Olivier Glass
Lecture Notes in Mathematics, Control of Partial Differential Equations 2048 131 (2012)
DOI: 10.1007/978-3-642-27893-8_3
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Local null controllability for a parabolic-elliptic system with local and nonlocal nonlinearities

Laurent Prouvée and Juan Límaco
Electronic Journal of Qualitative Theory of Differential Equations (74) 1 (2019)
DOI: 10.14232/ejqtde.2019.1.74
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Inverse Problems and Related Topics

Oleg Yu. Imanuvilov and Masahiro Yamamoto
Springer Proceedings in Mathematics & Statistics, Inverse Problems and Related Topics 310 101 (2020)
DOI: 10.1007/978-981-15-1592-7_6
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Recent Advances in Pure and Applied Mathematics

Enrique Fernández-Cara
RSME Springer Series, Recent Advances in Pure and Applied Mathematics 4 1 (2020)
DOI: 10.1007/978-3-030-41321-7_1
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A controllability result for a chemotaxis–fluid model

F.W. Chaves-Silva and S. Guerrero
Journal of Differential Equations 262 (9) 4863 (2017)
DOI: 10.1016/j.jde.2017.01.004
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Local exact controllability for the 1-d compressible Navier-Stokes equations

Sylvain Ervedoza
Séminaire Laurent Schwartz — EDP et applications 1 (2014)
DOI: 10.5802/slsedp.30
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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

Siddhartha Mishra and Roberto Molinaro
IMA Journal of Numerical Analysis 42 (2) 981 (2022)
DOI: 10.1093/imanum/drab032
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Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains

André da Rocha Lopes and Juan Límaco
Evolution Equations and Control Theory 11 (3) 749 (2022)
DOI: 10.3934/eect.2021024
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Global Controllability of the Navier–Stokes Equations in the Presence of Curved Boundary with No-Slip Conditions

Jiajiang Liao, Franck Sueur and Ping Zhang
Journal of Mathematical Fluid Mechanics 24 (3) (2022)
DOI: 10.1007/s00021-022-00689-0
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Approximate controllability of the FitzHugh-Nagumo equation in one dimension

Shirshendu Chowdhury, Mrinmay Biswas and Rajib Dutta
Journal of Differential Equations 268 (7) 3497 (2020)
DOI: 10.1016/j.jde.2019.10.001
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Local null controllability of the penalized Boussinesq system with a reduced number of controls

Jon Asier Bárcena-Petisco and Kévin Le Balc'h
Mathematical Control and Related Fields 12 (3) 641 (2022)
DOI: 10.3934/mcrf.2021038
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Null controllability of the N-dimensional Stokes system with N−1 scalar controls

Jean-Michel Coron and Sergio Guerrero
Journal of Differential Equations 246 (7) 2908 (2009)
DOI: 10.1016/j.jde.2008.10.019
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