An initial and boundary value problem modeling of fish-like swimming

Archive for Rational Mechanics and Analysis

Volumn 188, Issue 3, 2008, Pages 429-455

  Martín, Jorge San ^a   Scheid, Jean François ^b   Takahashi, Takéo ^b   Tucsnak, Marius ^b  

^a UNIVERSITY OF CHILE   (Chile)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42749097518     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-007-0092-2     Document Type: Article

References (36)

1. Borelli G. (1989) On the Movement of Animals. Springer, New York
2. Boukir K., Maday Y., Métivet B., Razafindrakoto E. (1997) A high-order characteristics/finite element method for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 25, 1421-1454
3. Boulakia M. (2003) Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid. C. R. Math. Acad. Sci. Paris 336, 985-990
4. Carling J., Williams T., Bowtell G. (1998) Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional Navier-Stokes equations and Newton's laws of motion. J. Exp. Biol. 201, 3143-3166
5. Chambolle A., Desjardins B., Esteban M.J., Grandmont C. (2005) Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. J. Math. Fluid Mech. 7, 368-404
6. Childress S. (1981) Mechanics of Swimming and Flying, vol. 2 of Cambridge Studies in Mathematical Biology. Cambridge University Press, Cambridge
7. Coutand D., Shkoller S. (2005) Motion of an elastic solid inside an incompressible viscous fluid. Arch. Ration. Mech. Anal. 176, 25-102
8. Coutand D., Shkoller S. (2006) The interaction between quasilinear elastodynamics and the Navier-Stokes equations. Arch. Ration. Mech. Anal. 179, 303-352
9. Cumsille P., Tucsnak P. (2006) Wellposedness of the Navier-Stokes flow in the exterior of the rotating obstacle. Math. Methods Appl. Sci. 29, 595-623
10. Cumsille, P., Takahashi, T.:Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid. Czechoslovak Math. J. (to appear)
11. Desjardins B., Esteban M., Grandmont C., Le Tallec P. (2001) Weak solutions for a fluid-elastic structure interaction model. Rev. Math. Comput. 14, 523-538
12. Desjardins B., Esteban M.J. (1999) Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal. 146, 59-71
13. Feireisl E. (2003) On the motion of rigid bodies in a viscous incompressible fluid. J. Evol. Equ. 3, 419-441
14. Galdi G. (1999) On the steady self-propelled motion of a body in a viscous incompressible fluid. Arch. Ration. Mech. Anal. 148, 53-88
15. Galdi G.P.: On the motion of a rigid body in a viscous liquid: a mathematical analysis with applications. In: Handbook of Mathematical Fluid Dynamics, Vol. I, pp. 653-791. North-Holland, Amsterdam, 2002
16. Gray J. (1932) Study in animal locomotion IV-the propulsive powers of the dolphin. J. Exp. Biol. 10, 192-199
17. Gray J. (1936) Study in animal locomotion I-the movement of a fish with special reference to the eel. J. Exp. Biol. 13, 88-104
18. Gunzburger M., Lee H.-C., Seregin G. (2000) Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. J. Math. Fluid Mech. 2, 219-266
19. Inoue A., Wakimoto M. (1977) On existence of solutions of the Navier-Stokes equation in a time dependent domain. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24, 303-319
20. Kanso E., Marsden J.E., Rowley C.W., Melli-Huber J.B. (2005) Locomotion of articulated bodies in a perfect fluid. J. Nonlin. Sci. 15, 255-289
21. Kelly S.D., Murray R.M. (1998) Modelling efficient pisciform swimming for control. Int. J. Robust Nonlin. Control 201, 3143-3166
22. Ladyzhenskaya O. (1969) The Mathematical Theory of Viscous Incomprehensible Flow. Gordon and Breach Science, New York
23. Leroyer A., Visonneau M. (2005) Numerical methods for ranse simulations of a self-propelled fish-like body. J. Fluids Struct. 20, 975-991
24. Lighthill J.: Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia, 1975
25. Lions J.-L., Magenes, E.: Non-homogeneous boundary value problems and applications, Vol. I. Springer, New York, 1972.
26. Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181
27. Liu H., Kawachi K. (1999) A numerical study of undulatory swimming swimming. J. Comput. Phys. 155, 223-247
28. Maury B., Glowinski R. (1997) Fluid-particle flow: a symmetric formulation. Acad C. R. Sci. Paris Sér. I Math. 324, 1079-1084
29. San Martín J., Scheid J.-F., Takahashi T., Tucsnak M. (2005) Convergence of the Lagrange-Galerkin method for the equations modelling the motion of a fluid-rigid system. SIAM J. Numer. Anal. 43, 1536-1571
30. San Martín J., Starovoitov V., Tucsnak M. (2002) Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Ration. Mech. Anal. 161, 113-147
31. Sparenberg J.A. (2002) Survey of the mathematical theory of fish locomotion. J. Eng. Math. 44, 395-448
32. Takahashi T. (2003) Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. Adv. Differ. Equ. 8, 1499-1532
33. Taylor, G.: Analysis of the swimming of long and narrow animals. Proc. R. Soc. Lond A. 214, (1952)
34. Temam R. (1983) Problèmes mathématiques en plasticité. Gauthier-Villars, Montrouge
35. Tryantafyllou M., Tryantafyllou G. (1995) An efficient swimming machine. Sci. Am. 272, 64-70
36. Wu, T.Y.: Mathematical biofluiddynamics and mechanophysiology of fish locomotion. Math. Methods Appl. Sci. 24, 1541-1564 (2001) Biofluiddynamics