Skip to main content
SpringerLink
Log in

On decay properties of the Stokes equations in exterior domains

  • Stokes Problems, Vector Potential Theory And Related Problems
  • Conference paper
  • First Online:
The Navier-Stokes Equations Theory and Numerical Methods

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

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, R. A.: Sobolev Spaces. New York-San Francisco-London: Academic Press 1975

    MATH  Google Scholar 

  2. Bogovski, M. E.: Solution of the first boundary value problem for the equation of continuity of an incompressible medium. Soviet Math. Dokl. 20 (1979) 1094–1098

    Google Scholar 

  3. Borchers, W., Sohr, H.: On the semigroup of the Stokes operator for exterior domains in Lq-spaces. Math. Z. 196 (1987) 415–425

    Article  MathSciNet  MATH  Google Scholar 

  4. Borchers, W., Sohr, H.: The equations divu=f and rotv=g with zero boundary conditions, to appear.

    Google Scholar 

  5. Cattabriga, L.: Su un problema al contorno relativo al sistema di equazioni di Stokes. Sem. Mat. Univ. Padova 31 (1964) 308–340

    MathSciNet  MATH  Google Scholar 

  6. Choquet-Bruhat, Y.: Elliptic systems in Hs,δ-spaces on manifolds which are Euklidic at infinity. Acta Math. 146 (1981) 129–150

    Article  MathSciNet  MATH  Google Scholar 

  7. Finn, R., Chang, D.: On the solutions of a class of equations occurring in continuum mechanics with application to the Stokes paradox. Arch. Rat. Mech. 7 (19) 389–401

    Google Scholar 

  8. Friedmann, A.: Partial differential equations. USA: Holt. Rinehart and Winston, Inc. 1969

    Google Scholar 

  9. Fujiwara, D., Morimoto, H.: An Lr-theorem of the Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 24 (1977) 685–700

    MathSciNet  MATH  Google Scholar 

  10. Galdi, G. P., Moremonti, P.: Monotonic decreasing and asymptotic behaviour of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains. Arch. Rat. Mech. Anal. 94 (1986) 253–266

    Article  MATH  Google Scholar 

  11. Giga, Y., Sohr, H.: On the Stokes operator in exterior domains, to appear in J. Fac. Sci. Univ. Tokyo 1989

    Google Scholar 

  12. Giroire, J.: Etude de quelques problemes aux limites exterieurs et resolution par equations integrales. Thèse de doctorat d'etat es sciences mathematiques. Paris 6: Universite Pierre et Marie Curie 1987

    Google Scholar 

  13. Miyakawa, T.: On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J. 12 (1982) 115–140

    MathSciNet  MATH  Google Scholar 

  14. Miyakawa, T., Sohr, H.: On energy inequality, smoothness and large time behaviour in L2 for weak solutions of Navier-Stokes equations. Math. Z. 199 (1988) 455–478

    Article  MathSciNet  MATH  Google Scholar 

  15. Sequeira, A.: Couplage entre la méthode des eléments finis et la méthode des équations intégrales. Application au problème exté rieur de Stokes stationnaire dans le plan. Thèse de doctorat de 3ème cycle. Paris 6: Université Pierre et Marie Curie 1981

    Google Scholar 

  16. Solonnikov, V. A.: Estimates for solutions of nonstationary Navier-Stokes equations. J. Soviet. Math. 8 (1977) 467–529

    Article  MATH  Google Scholar 

  17. Specovius-Neugebauer, M.: Exterior Stokes problem and decay at infinity. Math. Meth. Appl. Sci 8 (1986) 351–367

    Article  MathSciNet  MATH  Google Scholar 

  18. Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1965

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik-Informatik, Universität-GH-Paderborn, Warburger Straße 100, D-4790, Paderborn

    Hermann Sohr

  2. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D-6100, Darmstadt

    Werner Varnhorn

Authors
  1. Hermann Sohr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Werner Varnhorn
    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

Sohr, H., Varnhorn, W. (1990). On decay properties of the Stokes equations in exterior 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/BFb0086064

Download citation

  • DOI: https://doi.org/10.1007/BFb0086064

  • 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