Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 921-951. 
@article{AIHPC_2007__24_6_921_0,
     author = {Raymond, J.-P.},
     title = {Stokes and {Navier-Stokes} equations with nonhomogeneous boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {921--951},
     publisher = {Elsevier},
     volume = {24},
     number = {6},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.06.008},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.06.008/}
}
TY  - JOUR
AU  - Raymond, J.-P.
TI  - Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 921
EP  - 951
VL  - 24
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2006.06.008/
DO  - 10.1016/j.anihpc.2006.06.008
LA  - en
ID  - AIHPC_2007__24_6_921_0
ER  - 
%0 Journal Article
%A Raymond, J.-P.
%T Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 921-951
%V 24
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2006.06.008/
%R 10.1016/j.anihpc.2006.06.008
%G en
%F AIHPC_2007__24_6_921_0
Raymond, J.-P. Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 6, pp. 921-951. doi : 10.1016/j.anihpc.2006.06.008. https://www.numdam.org/articles/10.1016/j.anihpc.2006.06.008/

[1] Amann H., Nonhomogeneous Navier-Stokes equations with integrable low-regularity data, in: Birman , (Eds.), Nonlinear Problems in Mathematical Physics and Related Topics II, Kluwer Academic/Plenum Publishers, New York, 2002, pp. 1-28.

[2] Amann H., Navier-Stokes equations with nonhomogeneous Dirichlet boundary conditions, J. Nonlinear Math. Phys. 10 (Suppl. 1) (2003) 1-11.

[3] V. Barbu, I. Lasiecka, R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Mem. Amer. Math. Soc. (2006), in press. | Zbl

[4] Bensoussan A., Da Prato G., Delfour M.C., Mitter S.K., Representation and Control of Infinite Dimensional Systems, vol. 1, Birkhäuser, 1992. | MR | Zbl

[5] Bensoussan A., Da Prato G., Delfour M.C., Mitter S.K., Representation and Control of Infinite Dimensional Systems, vol. 2, Birkhäuser, 1993. | Zbl

[6] Dautray R., Lions J.-L., Analyse Mathématique et Calcul Numérique, vol. 8, Masson, Paris, 1988.

[7] R. Farwig, G.P. Galdi, H. Sohr, A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data, J. Math. Fluid Mech., published on line 27 October 2005. | Zbl

[8] Fursikov A.V., Gunzburger M.D., Hou L.S., Trace theorems for three-dimensional time-dependent solenoidal vector fields and their applications, Trans. Amer. Math. Soc. 354 (2001) 1079-1116. | MR | Zbl

[9] Fursikov A.V., Gunzburger M.D., Hou L.S., Inhomogeneous boundary value problems for the three-dimensional evolutionary Navier-Stokes equations, J. Math. Fluid Mech. 4 (2002) 45-75. | Zbl

[10] Galdi G.P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, vol. 1, Springer-Verlag, 1994. | Zbl

[11] Galdi G.P., Simader C.G., Sohr H., A class of solutions to the stationary Stokes and Navier-Stokes equations with boundary data in W1/q,q, Math. Ann. 331 (2005) 41-74. | Zbl

[12] Grisvard P., Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl. 45 (1966) 143-206, and 207-290. | Zbl

[13] Grubb G., Solonnikov V.A., Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods, Math. Scand. 69 (1991) 217-290. | Zbl

[14] Grubb G., Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity Lp Sobolev spaces, J. Math. Fluid Mech. 3 (2001) 57-81. | Zbl

[15] He J.-W., Glowinski R., Metcalfe R., Nordlander A., Periaux J., Active control and drag optimization for flow past a circular cylinder, J. Comp. Phys. 163 (2000) 83-117. | MR | Zbl

[16] Lasiecka I., Triggiani R., The regulator problem for parabolic equations with Dirichlet boundary control, Appl. Math. Optim. 16 (1987) 147-168. | MR | Zbl

[17] Lions J.-L., Espaces d'interpolation et domaines de puissances fractionnaires d'opérateurs, J. Math. Soc. Japan 14 (1962) 233-241. | MR | Zbl

[18] Lions J.-L., Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1969. | MR | Zbl

[19] Lions J.-L., Magenes E., Problèmes aux limites non homogènes, vol. 1, Dunod, Paris, 1968. | Zbl

[20] Lions J.-L., Magenes E., Problèmes aux limites non homogènes, vol. 2, Dunod, Paris, 1968. | Zbl

[21] Nguyen P.A., Raymond J.-P., Control problems for convection-diffusion equations with control localized on manifolds, ESAIM Control Optim. Calc. Var. 6 (2001) 467-488. | Numdam | MR | Zbl

[22] Raymond J.-P., Feedback boundary stabilization of the two-dimensional Navier-Stokes equations, SIAM J. Control Optim. 45 (2006) 790-828. | Zbl

[23] Raymond J.-P., Local boundary feedback stabilization of the Navier-Stokes equations, in: Control Systems: Theory, Numerics and Applications, http://pos.sissa.it.

[24] Solonnikov V.A., Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, in: Amer. Math. Soc. Transl. Ser. 2, vol. 75, 1968, pp. 1-116. | Zbl

[25] Temam R., Navier-Stokes Equations, North-Holland, 1984. | Zbl

[26] Troianiello G.M., Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. | MR | Zbl

[27] Von Wahl W., The Equations of Navier-Stokes and Abstract Parabolic Equations, Vieweg and Sohn, Braunschweig, 1985.

  • Badra, Mehdi; Raymond, Jean-Pierre Approximation of feedback gains for the Oseen system, Journal of Mathematical Analysis and Applications, Volume 549 (2025) no. 1, p. 129418 | DOI:10.1016/j.jmaa.2025.129418
  • Borachok, Ihor; Chapko, Roman; Johansson, B. Tomas Rothe’s method in combination with a fundamental sequences method for the nonstationary Stokes problem, Numerical Algorithms, Volume 96 (2024) no. 1, p. 59 | DOI:10.1007/s11075-023-01639-1
  • Reis, Timo; Schaller, Manuel Port-Hamiltonian Formulation of Oseen Flows, Systems Theory and PDEs (2024), p. 123 | DOI:10.1007/978-3-031-64991-2_5
  • Hamadi, M.A.; Jbilou, K.; Ratnani, A. An efficient extended block Arnoldi algorithm for feedback stabilization of incompressible Navier-Stokes flow problems, Applied Numerical Mathematics, Volume 174 (2022), p. 142 | DOI:10.1016/j.apnum.2022.01.011
  • Zhou, Kaiye; Gong, Wei Error Estimates for Finite Element Approximation of Dirichlet Boundary Control for Stokes Equations in L2(Γ), Journal of Scientific Computing, Volume 91 (2022) no. 2 | DOI:10.1007/s10915-022-01831-w
  • Eiter, Thomas; Hopf, Katharina; Mielke, Alexander Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation, Nonlinear Analysis: Real World Applications, Volume 65 (2022), p. 103491 | DOI:10.1016/j.nonrwa.2021.103491
  • Bathory, Michal; Stefanelli, Ulisse Variational resolution of outflow boundary conditions for incompressible Navier–Stokes, Nonlinearity, Volume 35 (2022) no. 11, p. 5553 | DOI:10.1088/1361-6544/ac8fd8
  • Biswas, A.; Tian, J.; Ulusoy, S. Error estimates for deep learning methods in fluid dynamics, Numerische Mathematik, Volume 151 (2022) no. 3, p. 753 | DOI:10.1007/s00211-022-01294-z
  • Gong, Wei; Mateos, Mariano; Singler, John; Zhang, Yangwen Analysis and Approximations of Dirichlet Boundary Control of Stokes Flows in the Energy Space, SIAM Journal on Numerical Analysis, Volume 60 (2022) no. 1, p. 450 | DOI:10.1137/21m1406799
  • Rodrigues, Sérgio S. Feedback Boundary Stabilization to Trajectories for 3D Navier–Stokes Equations, Applied Mathematics Optimization, Volume 84 (2021) no. S2, p. 1149 | DOI:10.1007/s00245-017-9474-5
  • Le Balc’h, Kévin; Tucsnak, Marius; Buttazzo, G.; Casas, E.; de Teresa, L.; Glowinski, R.; Leugering, G.; Trélat, E.; Zhang, X. A penalty approach to the infinite horizon LQR optimal control problem for the linearized Boussinesq system, ESAIM: Control, Optimisation and Calculus of Variations, Volume 27 (2021), p. 17 | DOI:10.1051/cocv/2021008
  • Fiorini, Camilla; Després, Bruno; Puscas, Maria Adela Sensitivity equation method for the Navier‐Stokes equations applied to uncertainty propagation, International Journal for Numerical Methods in Fluids, Volume 93 (2021) no. 1, p. 71 | DOI:10.1002/fld.4875
  • Casanova, Jean- Jérôme Fluid–structure system with boundary conditions involving the pressure, Journal of Evolution Equations, Volume 21 (2021) no. 1, p. 107 | DOI:10.1007/s00028-020-00581-2
  • Maity, Debayan; Takahashi, Takéo Lp Theory for the Interaction Between the Incompressible Navier–Stokes System and a Damped Plate, Journal of Mathematical Fluid Mechanics, Volume 23 (2021) no. 4 | DOI:10.1007/s00021-021-00628-5
  • Chaves-Silva, Felipe Wallison; Ervedoza, Sylvain; Souza, Diego A. Switching Controls for Analytic Semigroups and Applications to Parabolic Systems, SIAM Journal on Control and Optimization, Volume 59 (2021) no. 4, p. 2820 | DOI:10.1137/20m1356920
  • Hu, Weiwei An Approximating Control Design for Optimal Mixing by Stokes Flows, Applied Mathematics Optimization, Volume 82 (2020) no. 2, p. 471 | DOI:10.1007/s00245-018-9535-4
  • Badra, Mehdi; Mitra, Debanjana; Ramaswamy, Mythily; Raymond, Jean-Pierre Local feedback stabilization of time-periodic evolution equations by finite dimensional controls, ESAIM: Control, Optimisation and Calculus of Variations, Volume 26 (2020), p. 101 | DOI:10.1051/cocv/2020041
  • Benner, Peter; Trautwein, Christoph Optimal distributed and tangential boundary control for the unsteady stochastic Stokes equations, ESAIM: Control, Optimisation and Calculus of Variations, Volume 26 (2020), p. 62 | DOI:10.1051/cocv/2019042
  • Delay, Guillaume Existence of strong solutions to a fluid-structure system with a structure given by a finite number of parameters, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 54 (2020) no. 1, p. 301 | DOI:10.1051/m2an/2019059
  • Gong, Wei; Hu, Weiwei; Mateos, Mariano; Singler, John R.; Zhang, Yangwen Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 54 (2020) no. 6, p. 2229 | DOI:10.1051/m2an/2020015
  • Lequeurre, Julien; Munnier, Alexandre Vorticity and Stream Function Formulations for the 2D Navier–Stokes Equations in a Bounded Domain, Journal of Mathematical Fluid Mechanics, Volume 22 (2020) no. 2 | DOI:10.1007/s00021-019-0479-5
  • Mecherbet, Amina; Hillairet, Matthieu ESTIMATES FOR THE HOMOGENIZATION OF STOKES PROBLEM IN A PERFORATED DOMAIN, Journal of the Institute of Mathematics of Jussieu, Volume 19 (2020) no. 1, p. 231 | DOI:10.1017/s1474748018000014
  • Maity, Debayan; Raymond, Jean-Pierre; Roy, Arnab Maximal-in-Time Existence and Uniqueness of Strong Solution of a 3D Fluid-Structure Interaction Model, SIAM Journal on Mathematical Analysis, Volume 52 (2020) no. 6, p. 6338 | DOI:10.1137/18m1178451
  • Chang, Tongkeun; Jin, Bum Ja Initial-boundary value problem of the Navier–Stokes equations in the half space with nonhomogeneous data, ANNALI DELL'UNIVERSITA' DI FERRARA, Volume 65 (2019) no. 1, p. 29 | DOI:10.1007/s11565-018-0312-8
  • Gräßle, Carmen; Hinze, Michael; Lang, Jens; Ullmann, Sebastian POD model order reduction with space-adapted snapshots for incompressible flows, Advances in Computational Mathematics, Volume 45 (2019) no. 5-6, p. 2401 | DOI:10.1007/s10444-019-09716-7
  • Raymond, Jean-Pierre Stabilizability of Infinite Dimensional Systems by Finite Dimensional Control, Computational Methods in Applied Mathematics, Volume 19 (2019) no. 2, p. 267 | DOI:10.1515/cmam-2019-0026
  • Raymond, Jean-Pierre Stabilizability of Infinite-Dimensional Systems by Finite-Dimensional Controls, Computational Methods in Applied Mathematics, Volume 19 (2019) no. 4, p. 797 | DOI:10.1515/cmam-2018-0031
  • Mitra, Sourav Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel, ESAIM: Control, Optimisation and Calculus of Variations, Volume 25 (2019), p. 66 | DOI:10.1051/cocv/2019036
  • Badra, Mehdi; Takahashi, Takéo Boundary stabilization of a fluid-rigid body interaction system, IFAC-PapersOnLine, Volume 52 (2019) no. 2, p. 64 | DOI:10.1016/j.ifacol.2019.08.012
  • Chowdhury, Shirshendu; Ervedoza, Sylvain Open loop stabilization of incompressible Navier–Stokes equations in a 2d channel using power series expansion, Journal de Mathématiques Pures et Appliquées, Volume 130 (2019), p. 301 | DOI:10.1016/j.matpur.2019.01.006
  • Hu, Weiwei; Wu, Jiahong An approximating approach for boundary control of optimal mixing via Navier-Stokes flows, Journal of Differential Equations, Volume 267 (2019) no. 10, p. 5809 | DOI:10.1016/j.jde.2019.06.009
  • LIU, Hanbing; XIAO, Haijun Boundary feedback stabilization of Boussinesq equations, Acta Mathematica Scientia, Volume 38 (2018) no. 6, p. 1881 | DOI:10.1016/s0252-9602(18)30853-1
  • Phan, Duy; Rodrigues, Sérgio S. Stabilization to trajectories for parabolic equations, Mathematics of Control, Signals, and Systems, Volume 30 (2018) no. 2 | DOI:10.1007/s00498-018-0218-0
  • Chrysafinos, Konstantinos; Hou, L. Steven Semi-discrete error estimates of the evolutionary Stokes equations with inhomogeneous Dirichlet boundary data, Computers Mathematics with Applications, Volume 73 (2017) no. 8, p. 1684 | DOI:10.1016/j.camwa.2017.01.026
  • Badra, Mehdi; Takahashi, Takéo Feedback boundary stabilization of 2d fluid-structure interaction systems, Discrete Continuous Dynamical Systems - A, Volume 37 (2017) no. 5, p. 2315 | DOI:10.3934/dcds.2017102
  • Chrysafinos, Konstantinos; Hou, L. Steven Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 51 (2017) no. 4, p. 1501 | DOI:10.1051/m2an/2016070
  • Court, Sébastien Existence of 3D Strong Solutions for a System Modeling a Deformable Solid Inside a Viscous Incompressible Fluid, Journal of Dynamics and Differential Equations, Volume 29 (2017) no. 2, p. 737 | DOI:10.1007/s10884-015-9494-2
  • San Martín, Jorge; Schwindt, Erica L.; Takahashi, Takéo On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid, Journal of Inverse and Ill-posed Problems, Volume 25 (2017) no. 1, p. 1 | DOI:10.1515/jiip-2014-0056
  • Maity, Debayan; Raymond, Jean-Pierre Feedback Stabilization of the Incompressible Navier–Stokes Equations Coupled with a Damped Elastic System in Two Dimensions, Journal of Mathematical Fluid Mechanics, Volume 19 (2017) no. 4, p. 773 | DOI:10.1007/s00021-016-0305-2
  • Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity, Applied Mathematics Optimization, Volume 73 (2016) no. 3, p. 501 | DOI:10.1007/s00245-016-9345-5
  • Chang, Tongkeun; Jin, Bum Ja Initial and boundary value problem of the unsteady Navier–Stokes system in the half-space with Hölder continuous boundary data, Journal of Mathematical Analysis and Applications, Volume 433 (2016) no. 2, p. 1846 | DOI:10.1016/j.jmaa.2015.08.011
  • Chang, Tongkeun; Jin, Bum Ja Initial and boundary values for Lαq(Lp) solution of the Navier–Stokes equations in the half-space, Journal of Mathematical Analysis and Applications, Volume 439 (2016) no. 1, p. 70 | DOI:10.1016/j.jmaa.2016.02.052
  • Temam, Roger; Jung, Chang-Yeol; Gie, Gung-Min Recent progresses in boundary layer theory, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 5, p. 2521 | DOI:10.3934/dcds.2016.36.2521
  • Chang, Tongkeun; Jin, Bum Ja Solvability of the initial–boundary value problem of the Navier–Stokes equations with rough data, Nonlinear Analysis, Volume 125 (2015), p. 498 | DOI:10.1016/j.na.2015.05.032
  • Nguyen, Phuong Anh; Raymond, Jean-Pierre Boundary Stabilization of the Navier–Stokes Equations in the Case of Mixed Boundary Conditions, SIAM Journal on Control and Optimization, Volume 53 (2015) no. 5, p. 3006 | DOI:10.1137/13091364x
  • Bänsch, Eberhard; Benner, Peter; Saak, Jens; Weichelt, Heiko K. Riccati-based Boundary Feedback Stabilization of Incompressible Navier–Stokes Flows, SIAM Journal on Scientific Computing, Volume 37 (2015) no. 2, p. A832 | DOI:10.1137/140980016
  • Benner, Peter; Heiland, Jan Time-dependent Dirichlet conditions in finite element discretizations, ScienceOpen Research, Volume 0 (2015) no. 0 | DOI:10.14293/s2199-1006.1.sor-math.av2jw3.v1
  • Court, Sébastien Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system., Evolution Equations Control Theory, Volume 3 (2014) no. 1, p. 59 | DOI:10.3934/eect.2014.3.59
  • Court, Sébastien Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system., Evolution Equations Control Theory, Volume 3 (2014) no. 1, p. 83 | DOI:10.3934/eect.2014.3.83
  • Farwig, Reinhard; Kozono, Hideo Weak solutions of the Navier–Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality, Journal of Differential Equations, Volume 256 (2014) no. 7, p. 2633 | DOI:10.1016/j.jde.2014.01.029
  • Rodrigues, Sérgio S. Local exact boundary controllability of 3D Navier–Stokes equations, Nonlinear Analysis: Theory, Methods Applications, Volume 95 (2014), p. 175 | DOI:10.1016/j.na.2013.09.003
  • Liu, Hanbing Boundary optimal feedback controller for time-periodic Stokes–Oseen flows, Nonlinear Differential Equations and Applications NoDEA, Volume 21 (2014) no. 5, p. 709 | DOI:10.1007/s00030-013-0263-9
  • Jung, Ch-Y; Temam, R Boundary layer theory for convection-diffusion equations in a circle, Russian Mathematical Surveys, Volume 69 (2014) no. 3, p. 435 | DOI:10.1070/rm2014v069n03abeh004898
  • Юнг, Чанг-Юоль; Jung, Chang-Yeol; Темам, Роже; Temam, Roger Теория пограничного слоя для уравнений конвекции-диффузии в круге, Успехи математических наук, Volume 69 (2014) no. 3(417), p. 43 | DOI:10.4213/rm9584
  • Hamouda, Makram; Jung, Chang-Yeol; Temam, Roger Asymptotic analysis for the 3D primitive equations in a channel, Discrete Continuous Dynamical Systems - S, Volume 6 (2013) no. 2, p. 401 | DOI:10.3934/dcdss.2013.6.401
  • Chowdhury, Shirshendu; Ramaswamy, Mythily Optimal control of linearized compressible Navier–Stokes equations, ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 2, p. 587 | DOI:10.1051/cocv/2012023
  • Lequeurre, Julien Null Controllability of a Fluid-Structure System, SIAM Journal on Control and Optimization, Volume 51 (2013) no. 3, p. 1841 | DOI:10.1137/110839163
  • Badra, Mehdi 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 Continuous Dynamical Systems - A, Volume 32 (2012) no. 4, p. 1169 | DOI:10.3934/dcds.2012.32.1169
  • Amodei, L.; Buchot, J.‐M. A stabilization algorithm of the Navier–Stokes equations based on algebraic Bernoulli equation, Numerical Linear Algebra with Applications, Volume 19 (2012) no. 4, p. 700 | DOI:10.1002/nla.799
  • Farwig, R.; Kozono, H.; Sohr, H. Global Leray-Hopf Weak Solutions of the Navier-Stokes Equations with Nonzero Time-dependent Boundary Values, Parabolic Problems, Volume 80 (2011), p. 211 | DOI:10.1007/978-3-0348-0075-4_11
  • Badra, Mehdi; Takahashi, Takéo Stabilization of Parabolic Nonlinear Systems with Finite Dimensional Feedback or Dynamical Controllers: Application to the Navier–Stokes System, SIAM Journal on Control and Optimization, Volume 49 (2011) no. 2, p. 420 | DOI:10.1137/090778146
  • Dharmatti, Sheetal; Raymond, Jean-Pierre; Thevenet, Laetitia H∞ Feedback Boundary Stabilization of the Two-Dimensional Navier–Stokes Equations, SIAM Journal on Control and Optimization, Volume 49 (2011) no. 6, p. 2318 | DOI:10.1137/100782607
  • Lequeurre, Julien Existence of Strong Solutions to a Fluid-Structure System, SIAM Journal on Mathematical Analysis, Volume 43 (2011) no. 1, p. 389 | DOI:10.1137/10078983x
  • García, Galina C.; Takahashi, Takéo Inverse problem and null-controllability for parabolic systems, jiip, Volume 19 (2011) no. 3, p. 379 | DOI:10.1515/jiip.2011.036
  • John, Christian; Noack, Bernd R.; Schlegel, Michael; Tröltzsch, Fredi; Wachsmuth, Daniel Optimal Boundary Control Problems Related to High-Lift Configurations, Active Flow Control II, Volume 108 (2010), p. 405 | DOI:10.1007/978-3-642-11735-0_26
  • Farwig, R.; Kozono, H.; Sohr, H. Global Weak Solutions of the Navier-Stokes System with Nonzero Boundary Conditions, Funkcialaj Ekvacioj, Volume 53 (2010) no. 2, p. 231 | DOI:10.1619/fesi.53.231
  • Raymond, J.-P.; Vanninathan, M. Null controllability in a fluid–solid structure model, Journal of Differential Equations, Volume 248 (2010) no. 7, p. 1826 | DOI:10.1016/j.jde.2009.09.015
  • Raymond, Jean-Pierre Feedback Stabilization of a Fluid-Structure Model, SIAM Journal on Control and Optimization, Volume 48 (2010) no. 8, p. 5398 | DOI:10.1137/080744761
  • Casas, Eduardo; Mateos, Mariano; Raymond, Jean-Pierre Penalization of Dirichlet optimal control problems, ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 4, p. 782 | DOI:10.1051/cocv:2008049
  • Badra, Mehdi Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system, ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 4, p. 934 | DOI:10.1051/cocv:2008059
  • John, C.; Wachsmuth, D. Optimal Dirichlet Boundary Control of Stationary Navier–Stokes Equations with State Constraint, Numerical Functional Analysis and Optimization, Volume 30 (2009) no. 11-12, p. 1309 | DOI:10.1080/01630560903499001
  • Badra, Mehdi Lyapunov Function and Local Feedback Boundary Stabilization of the Navier–Stokes Equations, SIAM Journal on Control and Optimization, Volume 48 (2009) no. 3, p. 1797 | DOI:10.1137/070682630
  • Raymond, J.-P. Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations, Journal de Mathématiques Pures et Appliquées, Volume 87 (2007) no. 6, p. 627 | DOI:10.1016/j.matpur.2007.04.002

Cité par 73 documents. Sources : Crossref