Math. Model. Nat. Phenom.
Volume 16, 2021
Fluid-structure interaction
Article Number 9
Number of page(s) 26
Published online 03 March 2021
  1. H. Al Baba, N.V. Chemetov, Š. Nečasová and B. Muha, Strong solutions in L2 framework for fluid-rigid body interaction problem. Mixed case. Topol. Methods Nonlinear Anal. 52 (2018) 337–350. [Google Scholar]
  2. F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low Reynolds number swimmers : an example. J. Nonlinear Sci. 18 (2008) 277–302. [Google Scholar]
  3. T. Bodnár, G.P. Galdi and Š. Nečasová, Fluid-Structure Interaction and Biomedical Applications. Birkhäuser/Springer, Basel (2014). [Google Scholar]
  4. T. Bodnár, G.P. Galdi and Š. Nečasová, Particles in flows. Advances in Mathematical Fluid Mechanics. Birkhäuser/Springer, Cham (2017). [Google Scholar]
  5. F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. Vol. 183 of Applied Mathematical Sciences. Springer, New York (2013). [Google Scholar]
  6. A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids. Discrete Contin. Dyn. Syst. 20 (2008) 1–35. [Google Scholar]
  7. D. Bucur, E. Feireisl and Š. Nečasová, Boundary behavior of viscous fluids: influence of wall roughness and friction-driven boundary conditions. Arch. Ration. Mech. Anal. 197 (2010) 117–138. [Google Scholar]
  8. T. Chambrion and A. Munnier, locomotion and control of a self-propelled shape-changing body in a fluid. J. Nonlinear Sci. 21 (2011) 325–385. [Google Scholar]
  9. N.V. Chemetov and Š. Nečasová, The motion of the rigid body in the viscous fluid including collisions. Global solvability result. Nonlinear Anal. Real World Appl. 34 (2017) 416–445. [Google Scholar]
  10. C. Conca, J.S.M. H and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. Commun. Partial Differ. Equ. 25 (2000) 1019–1042. [Google Scholar]
  11. P. Cumsille and T. Takahashi, Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid. Czechoslovak Math. J. 58 (2008) 961–992. [Google Scholar]
  12. B. Desjardins, Global existence results for the incompressible density-dependent Navier-Stokes equations in the whole space. Differ. Integral Equ. 10 (1997) 587–598. [Google Scholar]
  13. B. Desjardins and M.J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal. 146 (1999) 59–71. [Google Scholar]
  14. B. Desjardins and M.J. Esteban, On weak solutions for fluid-rigid structure interaction : compressible and incompressible models. Commun. Partial Differ. Equ. 25 (2000) 1399–1413. [Google Scholar]
  15. R.J. DiPerna and P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989) 511–547. [Google Scholar]
  16. G. Galdi, On the steady self-propelled motion of a body in a viscous incompressible fluid. Arch. Rat. Mech. Anal. 148 (1999) 53–88. [Google Scholar]
  17. G.P. Galdi, On the motion of a rigid body in a viscous liquid : a mathematical analysis with applications, in Vol. I of Handbook of mathematical fluid dynamics. North-, Amsterdam (2002) 653–791. [Google Scholar]
  18. M. Geissert, K. Götze and M. Hieber, Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids. Trans. Am. Math. Soc. 365 (2013) 1393–1439. [Google Scholar]
  19. D. Gérard-Varet and M. Hillairet, Existence of weak solutions up to collision for viscous fluid-solid systems with slip. Commun. Pure Appl. Math. 67 (2014) 2022–2075. [Google Scholar]
  20. D. Gérard-Varet, M. Hillairet and C. Wang, The influence of boundary conditions on the contact problem in a 3d Navier-Stokes flow. J. Math. Pures Appl. 9 (2015) 1–38. [Google Scholar]
  21. D. Gérard-Varet and N. Masmoudi, Relevance of the slip condition for fluid flows near an irregular boundary. Commun. Math. Phys. 295 (2010) 99–137. [Google Scholar]
  22. M.D. Gunzburger, H.-C. Lee and G.A. Seregin, Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. J. Math. Fluid Mech. 2 (2000) 219–266. [Google Scholar]
  23. W. Jäger and A. Mikelić, On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differ. Equ. 170 (2001) 96–122. [Google Scholar]
  24. P.-L. Lions, Mathematical topics in fluid mechanics. Incompressible models. Vols. 1 and vol. 3 of Oxford Lecture Series in Mathematics and its Applications. The Clarendon Press, Oxford University Press, New York (1996). [Google Scholar]
  25. D. Maity and M. Tucsnak, Lp-Lq maximal regularity for some operators associated with linearized incompressible fluid-rigid body problems. Mathematical analysis in fluid mechanics–selected recent results. In Vol. 710 of Contemporary Mathematics. AMS Providence (2018) 175–201. [Google Scholar]
  26. J.A.S. 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]
  27. M. Padula, On the existence and uniqueness of nonhomogeneous motions in exterior domains. Math. Z. 203 (1990) 581–604. [Google Scholar]
  28. G. Planas and F. Sueur, On the “viscous incompressible fluid + rigid body” system with Navier conditions. Ann. Inst. Henri Poincaré Anal. Non Linéaire 31 (2014) 55–80. [Google Scholar]
  29. J. San Martín, T. Takahashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms. Quart. Appl. Math. 65 (2007) 405–424. [Google Scholar]
  30. D. Serre, Chute libre d’un solide dans un fluide visqueux incompressible. Jpn. J. Appl. Math. 4 (1987) 99–110. [Google Scholar]
  31. M. Sigalotti and J.-C. Vivalda, Controllability properties of a class of systems modeling swimming microscopic organisms. ESAIM: COCV 16 (2010) 1053–1076. [CrossRef] [EDP Sciences] [Google Scholar]
  32. A.L. Silvestre, On the self-propelled motion of a rigid body in a viscous liquid and on the attainability of steady symmetric self-propelled motions. J. Math. Fluid Mech. 4 (2002) 285–326. [Google Scholar]
  33. A.L. Silvestre, On the slow motion of a self-propelled rigid body in a viscous incompressible fluid. J. Math. Anal. Appl. 274 (2002) 203–227. [Google Scholar]
  34. J. Simon, Compact sets in the space Lp(0, T; B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
  35. J. Simon, Nonhomogeneous viscous incompressible fluids : existence of velocity, density, and pressure. SIAM J. Math. Anal. 21 (1990) 1093–1117. [Google Scholar]
  36. V.N. Starovoitov, Solvability of the problem of the self-propelled motion of several rigid bodies in a viscous incompressible fluid. Comput. Math. Appl. 53 (2007) 413–435. [Google Scholar]
  37. 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]
  38. C. Wang, Strong solutions for the fluid-solid systems in a 2-d domain. Asymptot. Anal. 89 (2014) 263–306. [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.