EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 27 (2021) ESAIM: COCV, 27 (2021) 65 References
Issue
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 65
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2021059
Published online 24 June 2021
  1. J.T. Beale, The initial value problem for the Navier-Stokes equations with a free surface. Commun. Pure Appl. Math. 34 (1981) 359–392. [CrossRef] [Google Scholar]
  2. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems, Second edition, Birkhäuser (2006). [Google Scholar]
  3. M. Boulakia, S. Guerrero and T. Takahashi, Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure. Nonlinearity 32 (2019) 3548–3592. [CrossRef] [Google Scholar]
  4. D. Coutand and S. Shkoller, Motion of an elastic solid inside an incompressible viscous fluid. Arch. Ratl. Mech. Anal. 176 (2005) 25–102. [CrossRef] [Google Scholar]
  5. P. Cumsille and T. Takahashi, Wellposedness for the system modeling the motion of a rigid body of arbitrary form in an incompressible viscous fluid. Czechoslovak Math. J. 58 (2008) 961–992. [CrossRef] [Google Scholar]
  6. S. Ervedoza and E. Zuazua, A systematic method for building smooth controls for smooth data. Discr. Continu. Dyn. Syst. B 14 (2010) 1375–1401. [Google Scholar]
  7. M. Fournié, M. Ndiaye and J.-P. Raymond, Feedback stabilization of a two-dimensional fluid-structure interaction system with mixed boundary conditions. SIAM J. Control Optim. 57 (2019) 3322–3359. [CrossRef] [Google Scholar]
  8. G. Grubb and V.A. Solonnikov, Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods. Math. Scand. 69 (1991) 217–290. [CrossRef] [Google Scholar]
  9. J. Haubner, M. Ulbrich and S. Ulbrich, Analysis of shape optimization problems for unsteady fluid-structure interaction. Inverse Problems 36 (2020) 034001. [CrossRef] [Google Scholar]
  10. J. Haubner, Shape optimization for fluid-structure interaction, Ph.D. Thesis, TUM, Germany (2020). [Google Scholar]
  11. M. Hieber and M. Murata, The Lp-approach to the fluid-rigid body interaction problem for compressible fluids. Evolut. Equ. Control Theory 4 (2015) 69–87. [CrossRef] [Google Scholar]
  12. M. Ignatova, I. Kukavica, I. Lasiecka and A. Tuffaha, On well-posedness for a free boundary fluid-structure model. J. Math. Phys. 53 (2012) 115624-1–13. [Google Scholar]
  13. M. Ignatova, I. Kukavica, I. Lasiecka and A. Tuffaha, On well-posedness and small data global existence for an interface damped free boundary fluid-structure model. Nonlinearity 27 (2014) 467–499. [CrossRef] [Google Scholar]
  14. I. Kukavica, A. Tuffaha and M. Ziane, Strong solutions to a Navier-Stokes-Lamé system on a domain with a non-flat boundary. Nonlinearity 24 (2011) 159–176. [CrossRef] [Google Scholar]
  15. I. Kukavica and A. Tuffaha, Solutions to a fluid-structure interaction free boundary problem. Discrete Cont. Dyn. Syst. 32 (2012) 1355–1389. [CrossRef] [Google Scholar]
  16. I. Kukavica and A. Tuffaha, Regularity of solutions to a free boundary problem of fluid-structure interaction. Indiana Univ. Math. J. 61 (2012) 1817–1859. [CrossRef] [Google Scholar]
  17. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol. 2, Dunod, Paris (1968). [Google Scholar]
  18. I. Lasiecka and Y. Lu, Interface feedback control stabilization of a nonlinear fluid–structure interaction. Nonlinear Anal. 75 (2012) 1449–1460. [CrossRef] [Google Scholar]
  19. D. Maity, J.-P. Raymond and A. Roy, Maximal-in-time existence of strong solutions of a 3D fluid structure interaction model. SIAM J. Math. Anal. 52 (2020) 6338–6378. [CrossRef] [Google Scholar]
  20. P.A. Nguyen and J.-P. Raymond, Boundary stabilization of the Navier-Stokes equations in the case of mixed boundary conditions. SIAM J. Control Optim. 53 (2015) 3006–3039. [CrossRef] [Google Scholar]
  21. J.-P. Raymond, Feedback stabilization of a fluid-structure model. SIAM J. Control Optim. 48 (2010) 5398–5443. [Google Scholar]
  22. J.-P. Raymond, Feedback boundary stabilization of the three-dimensional incompressible Navier-Stokes equations. J. Math. Pures Appl. 87 (2007) 627–669. [Google Scholar]
  23. J.-P. Raymond, Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition. Discrete Continu. Dyn. Syst. B 14 (2010) 1537–1564. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.-P. Raymond and L. Thevenet, Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. Discr. Continu. Dyn. Syst. A 27 (2010) 1159–1187. [CrossRef] [MathSciNet] [Google Scholar]
  25. 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]
  26. J.-P. Raymond, Stabilizability of infinite-dimensional systems by finite-dimensional controls. Comput. Methods Appl. Math. 19 (2019) 797–811. [Google Scholar]
  27. V.A. Solonnikov, Solvability of the problem of evolution of a viscous incompressible fluid bounded by a free surface on a finite time interval. St. Petersburg Math. J. 3 (1992) 189–220. [Google Scholar]
  28. T. Takahashi, M. Tucsnak and G. Weiss, Stabilization of a fluid-rigid body system. J. Differ. Equ. 259 (2015) 6459–6493. [Google Scholar]
  29. R. Temam, Navier-Stokes equations. Theory and numerical analysis, Reprint of the 1984 edition. AMS Chelsea Publishing, Providence, RI (2001). [Google Scholar]
  30. R. Temam, Navier-Stokes equations and nonlinear functional analysis, Second edition. CBMS-NSF Regional Conference Series in Applied Mathematics, 66. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1995). [Google Scholar]
  31. G. Troianiello, Elliptic differential equations and obstacle problems. The University Series in Mathematics. Plenum Press, New York (1987). [Google Scholar]
  32. X. Zhang and E. Zuazua, Long-time behavior of a coupled heat-wave system arising in fluid-structure interaction. Arch. Ratl. Mech. Anal. 184 (2007) 49–120. [Google Scholar]
  33. X. Zhang and E. Zuazua, Asymptotic behavior of a hyperbolic-parabolic coupled system arising in fluid-structure interaction. Free Boundary Problem. Boarding school. Ser. Number. Math. 154. Birkhäuser, Basel (2007) 445–455. [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.