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Applications of Mathematics

, Volume 47, Issue 6, pp 463–484 | Cite as

On the motion of rigid bodies in a viscous fluid

  • Eduard Feireisl
Article

Abstract

We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.

rigid body compressible fluid incompressible fluid global existence 

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References

  1. [1]
    B. Desjardins, M. J. Esteban: Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Rational Mech. Anal. 146 (1999), 59-71.Google Scholar
  2. [2]
    B. Desjardins, M. J. Esteban: On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models. Commun. Partial Differential Equations 25 (2000), 1399-1413.Google Scholar
  3. [3]
    R. J. DiPerna and P.-L. Lions: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989), 511-547.Google Scholar
  4. [4]
    E. Feireisl: On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable. Comment. Math. Univ. Carolinae 42 (2001), 83-98.Google Scholar
  5. [5]
    E. Feireisl: On the motion of rigid bodies in a viscous compressible fluid. Arch. Rational Mech. Anal. (2002). To appear.Google Scholar
  6. [6]
    E. Feireisl: On the motion of rigid bodies in a viscous incompressible fluid. J. Evolution Equations (2002). To appear.Google Scholar
  7. [7]
    E. Feireisl, A. Novotný and H. Petzeltová: On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids. J. Math. Fluid Dynamics 3 (2001), 358-392.Google Scholar
  8. [8]
    G. P. 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
  9. [9]
    V. Giovangigli: Multicomponent Flow Modeling. Birkhäuser, Basel, 1999.Google Scholar
  10. [10]
    M. D. Gunzburger, H. C. Lee and A. Seregin: Global existence of weak solutions for viscous incompressible flow around a moving rigid body in three dimensions. J. Math. Fluid Mech. 2 (2000), 219-266.Google Scholar
  11. [11]
    K.-H. Hoffmann, V. N. Starovoitov: Zur Bewegung einer Kugel in einer zäher Flüssigkeit. TUM-M9618, München, 1996.Google Scholar
  12. [12]
    P.-L. Lions: Mathematical Topics in Fluid Dynamics, Vol.2. Compressible models. Oxford Science Publication, Oxford, 1998.Google Scholar
  13. [13]
    K. R. Rajagopal, L. Tao: Mechanics of Mixtures. World Scientific, Singapore, 1995.Google Scholar
  14. [14]
    J. A. San Martin, V. Starovoitov and M. Tucsnak: Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Rational Mech. Anal. 161 (2002), 93-112.Google Scholar
  15. [15]
    D. Serre: Chute libre d'un solide dans un fluid visqueux incompressible. Existence. Jap. J. Appl. Math. 4 (1987), 99-110.Google Scholar
  16. [16]
    G. G. Stokes: On the effect of internal friction of fluids on the motion of pendulums. Trans. Cambridge Phil. Soc. 9 (1851), 80-85.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2002

Authors and Affiliations

  • Eduard Feireisl
    • 1
  1. 1.Mathematical Institute of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic

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