EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 27 (2021) Supplement ESAIM: COCV, 27 (2021) S18 References
Free Access
Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S18
Number of page(s) 51
DOI https://doi.org/10.1051/cocv/2020065
Published online 01 March 2021
  1. P. Albano and D. Tataru, Carleman estimates and boundary observability for a coupled parabolic-hyperbolic system. Electron. J. Differ. Equ. 2000 (2000) 1–15. [Google Scholar]
  2. M. Badra, S. Ervedoza and S. Guerrero, Local controllability to trajectories for non-homogeneous incompressible Navier-Stokes equations. Ann. Inst. Henri Poincaré Anal. Non Linéaire 33 (2016) 529–574. [CrossRef] [Google Scholar]
  3. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Systems & Control: Foundations & Applications, 2nd edn. Birkhäuser Boston, Inc., Boston, MA (2007). [Google Scholar]
  4. M. Boulakia and S. Guerrero, Local null controllability of a fluid-solid interaction problem in dimension 3. J. Eur. Math. Soc. (JEMS) 15 (2013) 825–856. [Google Scholar]
  5. M. Boulakia and A. Osses, Local null controllability of a two-dimensional fluid-structure interaction problem. ESAIM: COCV 14 (2008) 1–42. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, Vol. 183. Applied Mathematical Sciences. Springer, New York (2013). [CrossRef] [Google Scholar]
  7. M. Chapouly, On the global null controllability of a Navier-Stokes system with Navier slip boundary conditions. J. Differ. Equ. 247 (2009) 2094–2123. [Google Scholar]
  8. F.W. Chaves-Silva, R. Lionel and E. Zuazua, Null controllability of a system of viscoelasticity with a moving control. J. Math. Pures Appl. 101 (2014) 198–222. [Google Scholar]
  9. S.P. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 (1989) 15–55. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Chowdhury, D. Maity, M. Ramaswamy and J.-P. Raymond, Local stabilization of the compressible Navier-Stokes system, around null velocity, in one dimension. J. Differ. Equ. 259 (2015) 371–407. [Google Scholar]
  11. S. Chowdhury, M. Ramaswamy and J.-P. Raymond, Controllability and stabilizability of the linearized compressible Navier-Stokes system in one dimension. SIAM J. Control Optim. 50 (2012) 2959–2987. [Google Scholar]
  12. J.M. Coron and A.V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys. 4 (1996) 429–448. [Google Scholar]
  13. S. Ervedoza and M. Savel, Local boundary controllability to trajectories for the 1D compressible Navier Stokes equations. ESAIM: COCV 24 (2018) 211–235. [EDP Sciences] [Google Scholar]
  14. S. Ervedoza, O. Glass and S. Guerrero, Local exact controllability for the two- and three-dimensional compressible Navier-Stokes equations. Comm. Part. Differ. Equ. 41 (2016) 1660–1691. [Google Scholar]
  15. S. Ervedoza, O. Glass, S. Guerrero and J.-P. Puel, Local exact controllability for the one-dimensional compressible Navier-Stokes equation. Arch. Ration. Mech. Anal. 206 (2012) 189–238. [Google Scholar]
  16. C. Fabreand G. Lebeau, Prolongement unique des solutions de l’equation de Stokes. Comm. Part. Differ. Equ. 21 (1996) 573–596. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Feireisl, A. Novotný and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations. J. Math. Fluid Mech. 3 (2001) 358–392. [Google Scholar]
  18. E. Fernández-Cara, M. González-Burgos, S. Guerrero and J.-P. Puel. Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM: COCV 12 (2006) 442–465. [CrossRef] [EDP Sciences] [Google Scholar]
  19. E. Fernández-Cara, S. Guerrero, O. Yu. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501–1542. [Google Scholar]
  20. F. Flori and P. Orenga, On a nonlinear fluid-structure interaction problem defined on a domain depending on time. Nonlinear Anal. 38 (1999) 549–569. [Google Scholar]
  21. F. Flori and P. Orenga, Fluid-structure interaction: analysis of a 3-D compressible model. Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 753–777. [Google Scholar]
  22. X. Fu, X. Zhang and E. Zuazua, On the optimality of some observability inequalities for plate systems with potentials, in Phase Space Analysis of Partial Differential Equations, Vol. 69. Progr. Nonlinear Differential Equations Appl. Birkhäuser Boston, Boston, MA (2006) 117–132. [Google Scholar]
  23. A.V. Fursikov and O.Y. Imanuvilov, Controllability of Evolution Equations, Vol. 34. Lecture Notes Series. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  24. S. Guerrero, Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions. ESAIM: COCV 12 (2006) 484–544. [EDP Sciences] [Google Scholar]
  25. O. Imanuvilov and T. Takahashi, Exact controllability of a fluid-rigid body system. J. Math. Pures Appl. 87 (2007) 408–437. [Google Scholar]
  26. O. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations. ESAIM: COCV 6 (2001) 39–72. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  27. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I. Translated from the French by P. Kenneth. In Vol. 181 of Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  28. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. II. Translated from the French by P. Kenneth, In Vol. 182 of Die Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  29. P.-L. Lions, Mathematical Topics in Fluid Mechanics, Vol. 2, Vol. 10. Oxford Lecture Series in Mathematics and its Applications. Compressible Models, Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1998). [Google Scholar]
  30. S. Mitra, Analysis and Control of Some Fluid Models with Variable Density. Thèses, Université Toulouse III - Paul Sabatier. Available from https://tel.archives-ouvertes.fr/tel-01959694v1 (2018). [Google Scholar]
  31. S. Mitra, Carleman estimate for an adjoint of a damped beam equation and an application to null controllability. J. Math. Anal. Appl. 484 (2020) 123718. [Google Scholar]
  32. S. Mitra, Local existence of Strong solutions for a fluid-structure interaction model. J. Math. Fluid. Mech. 22 (2020) 60. [Google Scholar]
  33. N. Molina, Local exact boundary controllability for the compressible Navier-Stokes equations. SIAM J. Cont. Optim. 57 (2019) 2152–2184. [Google Scholar]
  34. K. Pileckas and W.M. Zajaczkowski, On the free boundary problem for stationary compressible Navier-Stokes equations. Comm. Math. Phys. 129 (1990) 169–204. [Google Scholar]
  35. J.-P. Raymond, Feedback stabilization of a fluid-structure model. SIAM J. Control Optim. 48 (2010) 5398–5443. [Google Scholar]
  36. J.-P. Raymond and M. Vanninathan, A fluid-structure model coupling the Navier-Stokes equations and the Lamé system. J. Math. Pures Appl. 102 (2014) 546–596. [Google Scholar]
  37. J.L. Rousseau and G. Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations. ESAIM: COCV 18 (2012) 712–747. [CrossRef] [EDP Sciences] [Google Scholar]
  38. R. Triggiani, Unique continuation from an arbitrary interior subdomain of the variable-coefficient Oseen equation. Nonlinear Anal. 71 (2009) 4967–4976. [Google Scholar]
  39. A. Valli and W.M. Zajaczkowski, Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case. Comm. Math. Phys. 103 (1986) 259–296. [Google Scholar]
  40. W.M. Zajaczkowski, On nonstationary motion of a compressible barotropic viscous fluid with boundary slip condition. J. Appl. Anal. 4 (1998) 167–204. [Google Scholar]
  41. X. Zhang, Exact controllability of semilinear plate equations. Asymptot. Anal. 27 (2001) 95–125. [Google Scholar]
  42. X. Zhang and E. Zuazua, A sharp observability inequality for Kirchhoff plate systems with potentials. Comput. Appl. Math. 25 (2006) 353–373. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.