Skip to main content
SpringerLink
Log in

Liouville Theorems for Stationary Flows of Shear Thickening Fluids in the Plane

  • Published:
Journal of Mathematical Fluid Mechanics Aims and scope Submit manuscript

Abstract

We consider entire solutions of the equations for stationary flows of shear thickening fluids in 2D and prove Liouville results under conditions like global boundedness of the velocity field or finiteness of the energy.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Acerbi E., Mingione G.: Regularity results for stationary electrorheological fluids. Arch. Ration. Mech. Anal. 164, 213–259 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fuchs M.: A note on non-uniformly elliptic Stokes-type systems in two variables. J. Math. Fluid Mech. 12, 266–279 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Fuchs, M.: Stationary flows of shear thickening fluids in 2D. J. Math. Fluid Mech. doi:10.1007/s00021-010-0044-8

  4. Fuchs, M., Seregin, G.: Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Lecture Notes in Mathematics, vol.1749, Springer, Berlin (2000)

  5. Galdi, G.: An introduction to the mathematical theory of the Navier–Stokes equations, vol.I, Springer Tracts in Natural Philosophy, vol.38, Springer, Berlin (1994)

  6. Galdi, G.: An introduction to the mathematical theory of the Navier-Stokes equations Vol.II, Springer Tracts in Natural Philosophy, vol.39, Springer, Berlin (1994)

  7. Giaquinta M., Modica G.: Nonlinear systems of the type of stationary Navier-Stokes system. J. Reine Angew. Math. 330, 173–214 (1982)

    MathSciNet  MATH  Google Scholar 

  8. Gilbarg D., Weinberger H.F.: Asymptotic properties of steady plane solutions of the Navier-Stokes equations with bounded Dirichlet integral. Ann. S.N.S. Pisa 5(4), 381–404 (1978)

    MathSciNet  MATH  Google Scholar 

  9. Koch, G.: Liouville theorem for 2D Navier–Stokes equations. Preprint

  10. Koch G., Nadirashvili N., Seregin G., Sverǎk V.: Liouville theorems for the Navier-Stokes equations and applications. Acta Math. 203, 83–105 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ladyzhenskaya O.A.: The mathematical theory of viscous incompressible flow. Gordon and Breach, New York (1969)

    MATH  Google Scholar 

  12. Málek J., Necǎs J., Rokyta M., Růžička M.: Weak and measure valued solutions to evolutionary PDEs. Chapman & Hall, London (1996)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität des Saarlandes, Fachbereich 6.1 Mathematik, Postfach 15 11 50, 66041, Saarbrücken, Germany

    Martin Fuchs

Authors
  1. Martin Fuchs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Fuchs.

Additional information

Communicated by G.P. Galdi

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fuchs, M. Liouville Theorems for Stationary Flows of Shear Thickening Fluids in the Plane. J. Math. Fluid Mech. 14, 421–444 (2012). https://doi.org/10.1007/s00021-011-0070-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00021-011-0070-1

Mathematics Subject Classification (2000)

Keywords

Search

Navigation