Skip to main content
SpringerLink
Log in
Book cover

Symposium on Non-Well-Posed Problems and Logarithmic Convexity pp 67–84Cite as

Some properties of solutions of the Navier-Stokes equations

  • Conference paper
  • First Online:

  • 302 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 316))

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   29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
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. S. Agmon, ‘Unicité et convexité dans les problèmes différenticls’ University of Montreal Press, (1966).

    Google Scholar 

  2. S. Agmon and L. Nirenberg, ‘Properties of solutions of ordinary differential equations in Banach space', Comm. Pure Appl. Math. 16 (1963), 121–239.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. J. Cohen and M. Lees, ‘Asymptotic decay of solutions of differential inequalities', Pacific J. Math. 11 (1961), 1235–1249.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. H. Dyer and D. E. Edmunds, ‘Lower bounds for solutions of the Navier-Stokes equations', Proc. London Math. Soc. 18 (1968), 169–178.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. H. Dyer and D. E. Edmunds, ‘On the regularity of solutions of the Navier-Stokes equations', J. London Math. Soc. 44 (1969), 93–99.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. H. Dyer and D. E. Edmunds, ‘Asymptotic behaviour of solutions of the stationary Navier-Stokes equations', J. London Math. Soc. 44 (1969), 340–346.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. E. Edmunds, ‘On the uniqueness of viscous flows', Arch. Rational Mech. Anal. 14 (1963), 171–176.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. E. Edmunds, ‘Asymptotic behaviour of solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 22 (1966), 15–21.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Graffi, ‘Sul teorema di unicità nella dinamica dei fluidi', Annali di Mat. 50 (1960), 379–388.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Hopf, ‘Über die Anfangswertaurgabe für die hydrodynamischen Grundgleichungen', Math. Nachrichten 4 (1951), 213–231.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Ito, ‘The existence and uniqueness of regular solution of non stationary Navier-Stokes equation', J. Fac. Sci. Univ. Tokyo, Sec. I, 9 (1961), 103–140.

    MathSciNet  MATH  Google Scholar 

  12. C. Kahane, ‘On the spatial analyticity of solutions of the Navier-Stokes equations’ Arch. Rational Mech. Anal. 33 (1969), 386–405.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Kampé de Fériet, ‘Sur la décroissance de l'énergie cinétique d'un fluide visqueux incompressible occupant un domaine borné ayant pour frontière des parois solides fixes', Ann. Soc. Sci. Bruxelles 63 (1949), 36–45.

    MATH  Google Scholar 

  14. S. Kaniel and M. Shinbrot, ‘Smoothness of weak solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 24 (1967), 302–324.

    MathSciNet  MATH  Google Scholar 

  15. A. A. Kiselev and O. A. Ladyzhenskaya, ‘On the existence and uniqueness of the solution of the nonstationary problem for a viscous incompressible fluid', Izv. Akad. Nauk. SSSR 21 (1957), 655–680.

    MathSciNet  Google Scholar 

  16. R. J. Knops and L. E. Payne, ‘On the stability of solutions of the Navier-Stokes equations backward in time', Arch. Rational Mech. Anal. 29 (1968), 331–335.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Lees and M. H. Protter, ‘Unique continuation for parabolic differential equations and inequalities', Duke Math. J. 28 (1961), 369–382.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Leray, ‘Étude de diverses équations integrales non linéaires et de quelques problèmes que pose l'hydrodynamique', J. Math. Pures Appl. 12 (1933), 1–82.

    MathSciNet  MATH  Google Scholar 

  19. J. Leray, ‘Essai sur les mouvements plans d'un liquide visqueux que limitent des parois', J. Math. Pures Appl. 13 (1934), 331–418.

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. K. Masuda, ‘On the exponential decay of solutions for some partial differential equations', J. Math. Soc. Japan 19 (1967), 82–90.

    Article  MathSciNet  MATH  Google Scholar 

  22. K. Masuda, ‘On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equations', Proc. Japan Acad. 43 (1967), 827–832.

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Ogawa, ‘Lower bounds for solutions of differential inequalities in Hilbert space', Proc. Amer. Math. Soc. 16 (1965), 1241–1243.

    Article  MathSciNet  MATH  Google Scholar 

  24. H. Ogawa, ‘On lower bounds and uniqueness for solutions of the Navier-Stokes equations', J. Math. Mech. 18 (1968), 445–452.

    MathSciNet  MATH  Google Scholar 

  25. H. Ogawa, ‘On the maximum rate of decay of solutions of parabolic differential inequalities', Arch. Rational Mech. Anal. 38 (1970), 173–177.

    Article  MathSciNet  MATH  Google Scholar 

  26. J. Serrin, ‘On the stability of viscous fluid motions', Arch. Rational Mech. Anal. 3 (1959), 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Serrin, ‘On the interior regularity of weak solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 9 (1962), 187–195.

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Serrin, ‘The initial value problem for the Navier-Stokes equations', Proc. Symp. Non-linear Problems, Univ. of Wisconsin (1963), 69–98.

    Google Scholar 

Download references

Authors
  1. R. H. Dyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

R. J. Knops

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag Berlin

About this paper

Cite this paper

Dyer, R.H. (1973). Some properties of solutions of the Navier-Stokes equations. In: Knops, R.J. (eds) Symposium on Non-Well-Posed Problems and Logarithmic Convexity. Lecture Notes in Mathematics, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069624

Download citation

  • DOI: https://doi.org/10.1007/BFb0069624

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06159-5

  • Online ISBN: 978-3-540-38370-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation