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Volumn 43, Issue 3, 2011, Pages 1345-1368

An existence and uniqueness result for the motion of self-propelled microswimmers

Author keywords

Dependence of solutions of PDEs on domain and boundary data; Low Reynolds number flows; Stokes equations; Swimming

Indexed keywords

BODY SHAPES; BOUNDARY DATA; BOUNDEDNESS; EXISTENCE AND UNIQUENESS; EXISTENCE AND UNIQUENESS RESULTS; EXTERNAL FORCE; INERTIAL EFFECT; INFINITE FLUIDS; INTEGRAL REPRESENTATION; LOW REYNOLDS NUMBER FLOW; REGULARITY ASSUMPTION; SELF PROPULSION; STOKES EQUATIONS; STOKES SYSTEM; SWIMMING; VELOCITY FIELD; VISCOUS FLUIDS; VISCOUS FORCES;

EID: 79960420817     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/10080083X     Document Type: Article
Times cited : (36)

References (24)
  • 1
    • 79952355859 scopus 로고    scopus 로고
    • Numerical strategies for stroke optimization of axisymmetric microswimmers
    • F. Alouges, A. DeSimone, and L. Heltai, Numerical strategies for stroke optimization of axisymmetric microswimmers, Math. Models Methods Appl. Sci., 21 (2011), pp. 361-387.
    • (2011) Math. Models Methods Appl. Sci. , vol.21 , pp. 361-387
    • Alouges, F.1    DeSimone, A.2    Heltai, L.3
  • 2
    • 84867972949 scopus 로고    scopus 로고
    • Optimal strokes for low Reynolds number swimmers: An example
    • F. Alouges, A. DeSimone, and A. Lefebvre, Optimal strokes for low Reynolds number swimmers: An example, J. Nonlinear Sci., 18 (2008), pp. 277-302.
    • (2008) J. Nonlinear Sci. , vol.18 , pp. 277-302
    • Alouges, F.1    DeSimone, A.2    Lefebvre, A.3
  • 3
    • 65449168343 scopus 로고    scopus 로고
    • Optimal strokes for axisymmetric microswimmers
    • F. Alouges, A. DeSimone, and A. Lefebvre, Optimal strokes for axisymmetric microswimmers, Eur. Phys. J. E, 28 (2009), pp. 279-284.
    • (2009) Eur. Phys. J. E , vol.28 , pp. 279-284
    • Alouges, F.1    DeSimone, A.2    Lefebvre, A.3
  • 4
    • 41649094383 scopus 로고    scopus 로고
    • Impulsive control of Lagrangian systems and locomotion in fluids
    • A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids, Discrete Contin. Dyn. Syst., 20 (2008), pp. 1-35.
    • (2008) Discrete Contin. Dyn. Syst. , vol.20 , pp. 1-35
    • Bressan, A.1
  • 6
    • 0004045998 scopus 로고
    • Cambridge Stud. Math. Biol., Cambridge University Press, Cambridge, UK
    • S. Childress, Mechanics of Swimming and Flying, Cambridge Stud. Math. Biol. 2, Cambridge University Press, Cambridge, UK, 1981.
    • (1981) Mechanics of Swimming and Flying , vol.2
    • Childress, S.1
  • 8
    • 0002816568 scopus 로고
    • An introduction to the mathematical theory of the navier-stokes equations
    • Springer-Verlag, New York
    • G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. 1 Linearized Steady Problems, Springer-Verlag, New York, 1994.
    • (1994) Linearized Steady Problems , vol.1
    • Galdi, G.P.1
  • 9
    • 0033436676 scopus 로고    scopus 로고
    • On the steady self-propelled motion of a body in a viscous incompressible fluid
    • G. P. Galdi, On the steady self-propelled motion of a body in a viscous incompressible fluid, Arch. Ration. Mech. Anal., 148 (1999), pp. 53-88.
    • (1999) Arch. Ration. Mech. Anal. , vol.148 , pp. 53-88
    • Galdi, G.P.1
  • 11
    • 0003983811 scopus 로고
    • 2nd ed., Robert E. Krieger Publishing, Huntington, NY
    • J. K. Hale, Ordinary Differential Equations, 2nd ed., Robert E. Krieger Publishing, Huntington, NY, 1980.
    • (1980) Ordinary Differential Equations
    • Hale, J.K.1
  • 13
    • 0002787294 scopus 로고
    • On uniqueness questions in the theory of viscous flow
    • J. G. Heywood, On uniqueness questions in the theory of viscous flow, Acta Math., 136 (1976), pp. 61-102.
    • (1976) Acta Math. , vol.136 , pp. 61-102
    • Heywood, J.G.1
  • 15
    • 0001809603 scopus 로고
    • Boundary value problems for a system in elasticity theory in unbounded domains. Korn inequalities
    • translation in Russian Math. Surveys, 43 (1988), pp. 65-119
    • V. A. Kondrat'ev and O. A. Oleǐnik, Boundary value problems for a system in elasticity theory in unbounded domains. Korn inequalities, Uspekhi Mat. Nauk, 43 (1988), pp. 55-98; translation in Russian Math. Surveys, 43 (1988), pp. 65-119.
    • (1988) Uspekhi Mat. Nauk , vol.43 , pp. 55-98
    • Kondrat'ev, V.A.1    Oleǐnik, O.A.2
  • 16
    • 70350589080 scopus 로고    scopus 로고
    • The hydrodynamics of swimming microorganisms
    • article 9
    • E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Progr. Phys., 72 (2009), article 9.
    • (2009) Rep. Progr. Phys. , vol.72
    • Lauga, E.1    Powers, T.R.2
  • 17
    • 84980072341 scopus 로고
    • On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers
    • M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Comm. Pure Appl. Math., 5 (1952), pp. 109-118.
    • (1952) Comm. Pure Appl. Math. , vol.5 , pp. 109-118
    • Lighthill, M.J.1
  • 19
    • 84890506631 scopus 로고
    • Life at low Reynolds number
    • E. M. Purcell, Life at low Reynolds number, Amer. J. Phys., 45 (1977), pp. 3-11.
    • (1977) Amer. J. Phys. , vol.45 , pp. 3-11
    • Purcell, E.M.1
  • 20
    • 46649086335 scopus 로고    scopus 로고
    • A control theoretic approach to the swimming of microscopic organisms
    • J. San Martín, T. Takahashi, and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms, Quart. Appl. Math., 65 (2007), pp. 405-424.
    • (2007) Quart. Appl. Math. , vol.65 , pp. 405-424
    • San Martín, J.1    Takahashi, T.2    Tucsnak, M.3
  • 21
    • 0024480808 scopus 로고
    • Geometry of self-propulsion at low Reynolds number
    • A. Shapere and F. Wilczek, Geometry of self-propulsion at low Reynolds number, J. Fluid Mech., 198 (1989), pp. 557-585.
    • (1989) J. Fluid Mech. , vol.198 , pp. 557-585
    • Shapere, A.1    Wilczek, F.2
  • 22
    • 0041849299 scopus 로고    scopus 로고
    • An Elementary Functional Analytic Approach Birkhäuser, Basel
    • H. Sohr, The Navier-Stokes Equations. An Elementary Functional Analytic Approach, Birkhäuser, Basel, 2001.
    • (2001) The Navier-Stokes Equations
    • Sohr, H.1
  • 23
    • 0000862974 scopus 로고
    • Analysis of the swimming of microscopic organisms
    • G. I. Taylor, Analysis of the swimming of microscopic organisms, Proc. Roy. Soc. Lond. Ser. A., 209 (1951), pp. 447-461.
    • (1951) Proc. Roy. Soc. Lond. Ser. A. , vol.209 , pp. 447-461
    • Taylor, G.I.1
  • 24
    • 0003887517 scopus 로고    scopus 로고
    • Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, RI
    • R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, RI, 2001.
    • (2001) Navier-Stokes Equations
    • Temam, R.1


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