Skip to main content
SpringerLink
Log in
Book cover

The Navier-Stokes Equations Theory and Numerical Methods pp 73–83Cite as

On large time behavior of the total kinetic energy for weak solutions of the Navier-Stokes equations in unbounded domains

  • Flows In Unbounded Domains
  • Conference paper
  • First Online:

  • 1237 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1431))

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Borchers, W., Miyakawa, T.: L2 Decay for the Navier-Stokes Flow in Halfspaces. Math. Ann. 282, 139–155 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Borchers,W., Miyakawa, T.: L2 Decay for the Navier-Stokes Flow in Unbounded Domains. Preprint (1986)

    Google Scholar 

  3. Borchers,W., Miyakawa, T.: Algebraic L2 Decay for Navier-Stokes Flows in Exterior Domains. Preprint (1988)

    Google Scholar 

  4. Friedman, A.: Partial differential equations. New York: Holt, Rinehart & Winston 1969

    MATH  Google Scholar 

  5. Fujita, H., Kato, T.: On the Navier-Stokes initial value problem I Arch.Rat.Mech.Anal. 16, 269–315 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4, 213–231 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kanwal, R.P.: Linear Integral Equations. Academic Press 1971

    Google Scholar 

  8. Kajikiya, R., Miyakawa, T.: On L2 Decay of Weak Solutions of the Navier-Stokes Equations in Rn. Math.Z. 192, 135–148 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  9. Komatsu, H.: Fractional Powers of Operators. Pacific J. of Math., Vol. 19, Nr. 2, 285–346 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ladyzhenskaya, O.A.: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach 1969

    Google Scholar 

  11. Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193–248 (1934)

    Article  MathSciNet  Google Scholar 

  12. Lions, J.-L.: Quelques methods de résolutions des problèmes aux limites nonlinéaires. Paris: Dunod et Gauthier-Villears 1969

    Google Scholar 

  13. Maremonti, P.: On the asymptotic behaviour of the L2-norm of suitable weak solutions to the Navier-Stokes equations in three-dimensional exterior domains. Comm.Math.Phys., 118, 335–400 (1988)

    Article  MathSciNet  Google Scholar 

  14. Rautmann, R.: Bemerkungen zur Anfangswertaufgabe einer stabilisierten Navier-Stokesschen Gleichung. ZAMM 55, T 217–221 (1975)

    MathSciNet  Google Scholar 

  15. Schonbek, M.E.: L2 decay for weak solutions of the Navier-Stokes equations. Arch. Rat. Mech. Anal. 88, 209–222 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wiegner, M.: Decay results for weak solutions of the Navier-Stokes equations in Rn. J. London Math. Soc. 35, 303–313 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik-Informatik der Universität-Gesmathochschule Paderborn, D-4790, Paderborn, Federal Republic of Germany

    Wolfgang Borchers

  2. Department of Mathematics, Faculty of Science, Hiroshima University, 730, Hiroshima, Japan

    Tetsuro Miyakawa

Authors
  1. Wolfgang Borchers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tetsuro Miyakawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

John G. Heywood Kyûya Masuda Reimund Rautmann Vsevolod A. Solonnikov

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Borchers, W., Miyakawa, T. (1990). On large time behavior of the total kinetic energy for weak solutions of the Navier-Stokes equations in unbounded domains. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086056

Download citation

  • DOI: https://doi.org/10.1007/BFb0086056

  • Received:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52770-1

  • Online ISBN: 978-3-540-47141-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation