On the steady self-propelled motion of a body in a viscous incompressible fluid

Archive for Rational Mechanics and Analysis

Volumn 148, Issue 1, 1999, Pages 53-88

  Galdi, Giovanni P ^a  

^a PA 15260   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033436676     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050156     Document Type: Article

References (51)

1. ADAMS, R. A., 1975, Sobolev Spaces, Academic Press, New York.
2. BABENKO, K. I., 1973, On Stationary Solutions of the Problem of Flow Past a Body of a Viscous Incompressible Fluid, Math. SSSR Sbornik, 20, 1-25.
3. BIRKHOFF G. & ZARANTONELLO, E. H., 1957, Jets, Wakes, and Cavities, Academic Press.
4. BLAKE, J. R., 1973, A Finite Model for Ciliated Micro-Organisms, J. Biomech., 6, 133-140.
5. BLAKE, J. R., & OTTO, S. R., 1996, Ciliary Propulsion, Chaotic Filtration and a 'Blinking' Stokeslet, J. Engineering Math., 30, 151-168.
6. BRENNEN, C., 1974, An Oscillating-Boundary-Layer Theory for Ciliary Propulsion, J. Fluid Mech., 65, 799-824.
7. BRENNEN, C., 1975, Hydromechanics of Propulsion for Ciliated Micro-Organisms. In Swimming and Flying in Nature, Vol. 1 (ed. T. Y. WU, C. BRENNEN & C. BROKAW), Plenum, 235-251.
8. BRENNEN, C. & WINET, H., 1977, Fluid Mechanics of Propulsion by Cilia and Flagella, Ann. Rev. Fluid Mech., 9, 339-398.
9. CHWANG, A.T. & WU, T. Y., 1975, Hydromechanics of Low-Reynolds-Number Flow. Part 2. Singularity Method for Stokes Flows, J. Fluid Mech., 67, 787-815.
10. CHILDRESS, S., 1981, Mechanics of Swimming and Flying, Cambridge University Press.
11. FELDERHOF, B.U. & JONES, R. B., 1994, Inertial Effects in Small-Amplitude Swimming of a Finite Body, Physica A, 202, 94-118.
12. FELDERHOF, B. U. & JONES, R. B., 1994, Small-Amplitude Swimming of a Sphere, Physica A, 202, 119-144.
13. FINN, R., 1965, On the Exterior Stationary Problem for the Navier-Stokes Equations, and Associated Perturbation Problems, Arch. Rational Mech. Anal., 19, 363-406.
14. FUJITA, H., 1961, On the Existence and Regularity of the Steady-State Solutions of the Navier-Stokes Equation, J. Fac. Sci. Univ. Tokyo, (1A) 9, 59-102.
15. GALDI, G. P., 1998, On the Steady, Translational Self-Propelled Motion of a Symmetric Body in a Navier-Stokes Fluid, Quaderni di Matematica della II Università di Napoli, Vol I, to be published.
16. GALDI, G. P., 1998, On the Steady Translational Self-Propelled Motion of a Body in a Navier-Stokes Fluid, Proc. Conf. Equadiff 9, Brno, Czech Rep., to be published.
17. GALDI, G. P., 1998, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Linearized Steady Problems, Revised Edition, Springer-Verlag.
18. GALDI, G. P., 1998, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Nonlinear Steady Problems, Revised Edition, Springer-Verlag.
19. GALDI, G. P., HEYWOOD, J. G. & SHIBATA, Y., 1997, On the Global Existence and Convergence to Steady State of Navier-Stokes Flow Past an Obstacle that is Started from the Rest, Arch. Rational Mech. Anal., 138, 307-318.
20. GALDI, G. P. & MAREMONTI, P., 1986, Monotonic Decreasing and Asymptotic Behavior of the Kinetic Energy for Weak Solutions of the Navier-Stokes Equations in Exterior Domains, Arch. Rational Mech. Anal. 94, 253-266.
21. GRAY, J., 1968, Animal Locomotion, Weidenfeld and Nicolson, London.
22. HAPPEL, V. & BRENNER, H., 1965, Low Reynolds Number Hydrodynamics, Prentice Hall.
23. HEYWOOD, J. G., 1972 The Exterior Nonstationary Problem for the Navier-Stokes Equations, Acta Math., 129, 11-34.
24. KELLER, S. R. & WU, T. Y., 1977, A Porous Prolate-Spheroidal Model for Ciliated Micro-Organisms, J. Fluid Mech., 80, 259-278.
25. KONDRAT'EV, V. A. & OLEINIK, O. A., 1988, Boundary-Value Problems for the System of Elasticity Theory in Unbounded Domains. Korn's Inequalities, Russian Math. Surveys, 43, 65-119.
26. KOZONO, H. & SOHR, H., 1993, On Stationary Navier-Stokes Equations in Unbounded Domains, Ricerche Mat., 42, 69-86.
27. KOZONO, H., SOHR, H. & YAMAZAKI, M., 1997, Representation Formula, Net Force and Energy Relation to the Stationary Navier-Stokes Equations in 3-Dimensional Exterior Domains, Kyushu J. Math., 51, 239-260.
28. LADYZHENSKAYA, O. A., 1959, Investigation of the Navier-Stokes Equation for a Stationary Flow of an Incompressible Fluid, Uspehi Mat. Nauk. (3) 14, 75-97 (in Russian).
29. LAMB, H., 1932, Hydrodynamics, Cambridge University Press.
30. LERAY, J., 1933, Étude de Diverses Équations Intégrales non Linéaires et de Quelques Problème que Pose l'Hydrodynamique, J. Math. Pures Appl., 12, 1-82.
31. LOITSYANSKII, L. G., 1966, Mechanics of Liquids and Gases, Pergamon Press.
32. LUGOVTSOV, A. A. & LUGOVTSOV, B. A., 1971, Example of a Viscous Incompressible Flow Past a Body with Moving Boundary, Dynamics of Continuous Media, Novosibirsk, 8, 49-55 (in Russian).
33. MILNE-THOMSON, L. M., 1952, Theoretical Aerodynamics, Van Nostrandt, New York.
34. MOISEYEV, N. N. & RUMYANTSEV, V. V., 1968, Dynamic Stability of Bodies Containing Fluid, Springer-Verlag New York.
35. PUKHNACHEV, V. V., 1989, Asymptotics of a Velocity Field at Considerable Distances From a Self Propelled Body, J. Appl. Mech. Tech. Phys., 30, 52-60.
36. PUKHNACHEV, V. V., 1990, Stokes Approximation in a Problem of the Flow Around a Self-Propelled Body, Boundary Value Problems in Mathematical Physics, Naukova Dumka, Kiev, 65-73 (in Russian).
37. PUKHNACHEV, V. V., 1990, The Problem of Momentumless Flow for the Navier-Stokes Equations, Springer Lecture Notes in Mathematics, 1431, 87-94.
38. SAUER, N., 1972, The Steady State Navier-Stokes Equations for Incompressible Flows with Rotating Boundary, Proc. Roy. Soc. Edinburgh, 110A, 93-99.
39. SENNITSKII, V. L., 1978, Liquid Flow Around a Self-Propelled Body, J. Appl. Mech. Tech. Phys., 3, 15-27.
40. SENNITSKII, V. L., 1984, An Example of Axisymmetric Fluid Flow Around a Self-Propelled Body, J. Appl. Mech. Tech. Phys., 25, 526-530.
41. SENNITSKII, V. L., 1990, Self-Propulsion of a Body in a Fluid, J. Appl. Mech. Tech. Phys., 31, 266-272.
42. SERRE, D., 1987, Chute Libre d'un Solide dans un Fluide Visqueux Incompressible. Existence, Jap. J. Appl. Math., 4, 99-110.
43. SERRIN, J. B., 1959, Mathematical Principles of Classical Fluid Mechanics, Handbuch der Physik, Bd VIII/I, Springer-Verlag, Berlin-Heidelberg-New York, 125-263.
44. SHAPERE, A. & WILCZEK, F., 1989, Geometry of Self-Propulsion at Low Reynolds Number, J. Fluid Mech., 198, 557-585.
45. SOBOLEV, S. L., 1963, Applications of Functional Analysis to Mathematical Physics, Amer. Math. Soc., Providence.
46. TAYLOR, G. I., 1951, Analysis of the Swimming of Microscopic Organisms, Proc. Royal Soc. London A, 209, 447-461.
47. WEINBERGER, H. F., 1972, Variational Properties of Steady fall in Stokes Flow, J. Fluid Mech., 52, 321-344.
48. WEINBERGER, H. F., 1974, Variational Principles for a Body Falling in Steady Stokes Flow, Proc. Symp. on Continuum Mechanics and Related Problems of Analysis, 2, Mecniereba, 330-339.
49. WEINBERGER, H. F., 1973, On the Steady Fall of a Body in a Navier-Stokes Fluid, Proc. Symp. Pure Mathematics, 23, 421-440.
50. ZAGNIBEVA, I. G., 1978, The Solvability of the Problem of the Dynamics of a Solid Body with a Cavity Containing a Viscous Fluid, Dokl. Akad. Nauk SSSR, 238 (5), 1075 (in Russian).
51. ZAGNIBEVA, I.G. & LJUL'KA, V. A., 1978, Motion of a Solid Filled with a Viscous Fluid Under the Action of an Arbitrary System of Forces and Moments, Direct Numerical Simulation of Gas Flows; Numerical Simulation; Gas Dynamics, Edited by O. M. BELOCERKOVSKII, Akad. Nauk SSSR, Vychisl. Tsentr, Moscow, 145 (in Russian).