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2013 | 23 | 2 | 277-290

Tytuł artykułu

The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids.

Rocznik

Tom

23

Numer

2

Strony

277-290

Opis fizyczny

Daty

wydano
2013
otrzymano
2012-04-19
poprawiono
2012-10-18
poprawiono
2013-01-14

Twórcy

  • Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USA

Bibliografia

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  • Childress, S. (1981). Mechanics of Swimming and Flying, Cambridge University Press, Cambridge.
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  • Fukuda, T., Kawamoto, A., Arai, F. and Matsuura, H. (1995). Steering mechanism and swimming experiment of micro mobile robot in water, Proceedings of Micro Electro Mechanical Systems (MEMS'95), Amsterdam, The Netherlands, pp. 300-305.
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  • Hawthorne, M.F., Zink, J.I., Skelton, J.M., Bayer, M.J., Liu, Ch., Livshits, E., Baer, R. and Neuhauser, D. (2004). Electrical or photocontrol of rotary motion of a metallacarborane, Science 303: 1849.
  • Happel, V. and Brenner, H. (1965). Low Reynolds Number Hydrodynamics, Prentice Hall, Upper Saddle River, NJ.
  • Hirose, S. (1993). Biologically Inspired Robots: Snake-like Locomotors and Manipulators, Oxford University Press, Oxford.
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  • Khapalov, A.Y. (1999). Approximate controllability properties of the semilinear heat equation with lumped controls, International Journal of Applied Mathematics and Computer Science 9(4): 751-765.
  • Khapalov, A.Y. (2005). The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, Technical Report 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5.pdf.
  • Khapalov, A.Y. and Eubanks, S. (2009). The wellposedness of a 2-D swimming model governed in the nonstationary Stokes fluid by multiplicative controls, Applicable Analysis 88: 1763-1783, DOI:10.1080/00036810903401222.
  • Khapalov, A.Y. (2010). Controllability of Partial Differential Equations Governed by Multiplicative Controls, Lecture Notes in Mathematics Series, Vol. 1995, Springer-Verlag, Berlin/Heidelberg.
  • Khapalov, A.Y. and Trinh, G. (2013). Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid, Discrete and Continuous Dynamical Systems Series A 33: 1513-1544.
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  • Peskin, C.S. (1977). Numerical analysis of blood flow in the heart, Journal of Computational Physics 25: 220-252.
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Bibliografia

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