Free Access
Volume 54, Number 1, January-February 2020
Page(s) 301 - 333
Published online 31 January 2020
  1. R.A. Adams, Sobolev spaces. In: Vol. 65 of Pure and Applied Mathematics. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1975). [Google Scholar]
  2. L. Baffico, C. Grandmont and B. Maury, Multiscale modeling of the respiratory tract. Math. Models Methods Appl. Sci. 20 (2010) 59–93. [Google Scholar]
  3. Y. Bazilevs, K. Takizawa and T.E. Tezduyar, Computational Fluid-Structure Interaction, Methods and Applications. Wiley (2013). [CrossRef] [Google Scholar]
  4. H. Beirão da Veiga, On the existence of strong solutions to a coupled fluid-structure evolution problem. J. Math. Fluid Mech. 6 (2004) 21–52. [CrossRef] [MathSciNet] [Google Scholar]
  5. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems, 2nd edition. In: Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc, Boston, MA (2007). [CrossRef] [Google Scholar]
  6. M. Boulakia, Existence of weak solutions for the three-dimensional motion of an elastic structure in an incompressible fluid. J. Math. Fluid Mech. 9 (2007) 262–294. [CrossRef] [Google Scholar]
  7. M. Boulakia and S. Guerrero, A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 777–813. [CrossRef] [Google Scholar]
  8. M. Boulakia and S. Guerrero, Regular solutions of a problem coupling a compressible fluid and an elastic structure. J. Math. Pures Appl. 94 (2010) 341–365. [Google Scholar]
  9. M. Boulakia and S. Guerrero, On the interaction problem between a compressible fluid and a Saint-Venant Kirchhoff elastic structure. Adv. Differ. Equ. 22 (2017) 1–48. [Google Scholar]
  10. M. Boulakia, E.L. Schwindt and T. Takahashi, Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid. Interfaces Free Bound. 14 (2012) 273–306. [CrossRef] [Google Scholar]
  11. L. Bălilescu, J. San Martín and T. Takahashi, Fluid-rigid structure interaction system with Coulomb’s law. SIAM J. Math. Anal. 49 (2017) 4625–4657. [CrossRef] [Google Scholar]
  12. A. Chambolle, B. Desjardins, M.J. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. J. Math. Fluid Mech. 7 (2005) 368–404. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972). Travaux et Recherches Mathématiques, No. 21. [Google Scholar]
  14. G.P. Galdi, An introduction to the mathematical theory of the Navier–Stokes equations, 2nd edition. In: Springer Monographs in Mathematics. Springer, New York (2011). [CrossRef] [Google Scholar]
  15. C. Grandmont and Y. Maday, Existence for an unsteady fluid–structure interaction problem. M2AN Math. Model. Numer. Anal. 34 (2000) 609–636. [CrossRef] [Google Scholar]
  16. P. Grisvard, Elliptic problems in nonsmooth domains. In: Vol. 69 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2011). [Google Scholar]
  17. M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow. Comm. Partial Differ. Equ. 32 (2007) 1345–1371. [CrossRef] [MathSciNet] [Google Scholar]
  18. J.G. Houot, J. San Martin and M. Tucsnak, Existence of solutions for the equations modeling the motion of rigid bodies in an ideal fluid. J. Funct. Anal. 259 (2010) 2856–2885. [Google Scholar]
  19. J. Lequeurre, Existence of strong solutions to a fluid-structure system. SIAM J. Math. Anal. 43 (2011) 389–410. [CrossRef] [Google Scholar]
  20. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. In: Vol. 1 of Travaux et Recherches Mathématiques, No. 17. Dunod, Paris (1968). [Google Scholar]
  21. Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid-structure interaction model. ESAIM Control Optim. Calc. Var. 19 (2013) 20–42. [CrossRef] [Google Scholar]
  22. D. Maity, T. Takahashi and M. Tucsnak, Analysis of a system modelling the motion of a piston in a viscous gas. J. Math. Fluid Mech. 19 (2017) 551–579. [CrossRef] [Google Scholar]
  23. V. Maz’ya and J. Rossmann, Elliptic equations in polyhedral domains. In: Vol. 162 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  24. Š. Nečasová, T. Takahashi and M. Tucsnak, Weak solutions for the motion of a self-propelled deformable structure in a viscous incompressible fluid. Acta Appl. Math. 116 (2011) 329–352. [Google Scholar]
  25. 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. [Google Scholar]
  26. A. Pazy, Semigroups of linear operators and applications to partial differential equations. In: Vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983). [CrossRef] [Google Scholar]
  27. J.-P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 921–951. [CrossRef] [MathSciNet] [Google Scholar]
  28. 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]
  29. J. San Martín, J.-F. Scheid, T. Takahashi and M. Tucsnak, An initial and boundary value problem modeling of fish-like swimming. Arch. Ration. Mech. Anal. 188 (2008) 429–455. [Google Scholar]
  30. J.A. San Martín, V. Starovoitov and M. Tucsnak, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Ration. Mech. Anal. 161 (2002) 113–147. [Google Scholar]
  31. H. Sohr, The Navier–Stokes equations. In: Birkhäuser Advanced Texts: Basler Lehrbücher [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser Verlag, Basel (2001). [CrossRef] [Google Scholar]
  32. T. Takahashi, Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. Adv. Differ. Equ. 8 (2003) 1499–1532. [Google Scholar]
  33. T. Takahashi, M. Tucsnak and G. Weiss, Stabilization of a fluid-rigid body system. J. Differ. Equ. 259 (2015) 6459–6493. [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.

Recommended for you