Skip to main content

Do Navier-Stokes Equations Enable to Predict Contact Between Immersed Solid Particles?

  • Conference paper
Analysis and Simulation of Fluid Dynamics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

We present here a short overview of recent results on a paradox appearing in the area of fluid-solid interactions. This paradox states that, in two space dimensions, strong solutions to viscous models describing fluid-solid interactions do not permit rigid solids inside the fluid to collide.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Desjardins and M.J. Esteban. Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal., 146(1):59–71, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  2. E. Feireisl. On the motion of rigid bodies in a viscous fluid. Appl. Math., 47(6):463–484, 2002. Mathematical theory in fluid mechanics (Paseky, 2001).

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Feireisl. On the motion of rigid bodies in a viscous fluid. Appl. Math., 47(6):463–484, 2002. Mathematical theory in fluid mechanics (Paseky, 2001).

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Feireisl. On the motion of rigid bodies in a viscous compressible fluid. Arch. Ration. Mech. Anal., 167(4):281–308, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Grisvard. Elliptic problems in nonsmooth domains, volume 24 of Monographs and. Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA, 1985.

    MATH  Google Scholar 

  6. M.D. Gunzburger, H.-C. Lee, and G.A. Seregin. Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. J. Math. Fluid Mech., 2(3):219–266, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Hillairet. Aspects interactifs de la mécanique des fluides. PhD thesis, Ecole Normale Supérieure de Lyon, 2005.

    Google Scholar 

  8. M. Hillairet. Asymptotic collision between solid particles in a Burgers-Hopf fluid. Asymptotic analysis, In press.

    Google Scholar 

  9. M. Hillairet and D. Serre. Chute stationnaire d’un solide dans un fluide visqueux incompressible le long d’un plan incliné. Ann. Inst. H. Poincaré Anal. Non Linéaire, 20(5):779–803, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Hillairet and J.L. VĂ zquez. A first no-collision result in two dimensions. In preparation, 2005.

    Google Scholar 

  11. J.A. San Martín, V. Starovoitov, and M. Tucsnak. Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Ration. Mech. Anal., 161(2):113–147, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  12. V.N. Starovoitov. On the nonuniqueness of the solution of the problem of the motion of a rigid body in a viscous incompressible fluid. Zap. Nauchn. Sem. St.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI), 306(Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funktsii. 34):199–209, 231–232, 2003.

    Google Scholar 

  13. V.N. Starovoitov. Behavior of a rigid body in an incompressible viscous fluid near a boundary. In Free boundary problems (Trento, 2002), volume 147 of Internat. Ser. Numer. Math., pages 313–327. Birkhäuser, Basel, 2004.

    Google Scholar 

  14. Takéo Takahashi. Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. Adv. Differential Equations, 8(12):1499–1532, 2003.

    MATH  MathSciNet  Google Scholar 

  15. J.L. Vàzquez and E. Zuazua. Large time behavior for a simplified 1D model of fluid-solid interaction. Comm. Partial Differential Equations, 28(9–10):1705–1738, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  16. J.L. VĂ zquez and E. Zuazua. Lack of collision in a simplified 1-d model for fluid-solid interaction. Preprint, may 2004.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Hillairet, M. (2006). Do Navier-Stokes Equations Enable to Predict Contact Between Immersed Solid Particles?. In: Calgaro, C., Coulombel, JF., Goudon, T. (eds) Analysis and Simulation of Fluid Dynamics. Advances in Mathematical Fluid Mechanics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7742-7_7

Download citation

Publish with us

Policies and ethics