Advertisement

Some properties of solutions of the Navier-Stokes equations

  • R. H. Dyer
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 316)

Keywords

Weak Solution Differential Inequality Unique Continuation Parabolic Differential Equation Unique Continuation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Agmon, ‘Unicité et convexité dans les problèmes différenticls’ University of Montreal Press, (1966).Google Scholar
  2. 2.
    S. Agmon and L. Nirenberg, ‘Properties of solutions of ordinary differential equations in Banach space', Comm. Pure Appl. Math. 16 (1963), 121–239.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P. J. Cohen and M. Lees, ‘Asymptotic decay of solutions of differential inequalities', Pacific J. Math. 11 (1961), 1235–1249.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    D. E. Edmunds, ‘On the uniqueness of viscous flows', Arch. Rational Mech. Anal. 14 (1963), 171–176.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D. E. Edmunds, ‘Asymptotic behaviour of solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 22 (1966), 15–21.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    D. Graffi, ‘Sul teorema di unicità nella dinamica dei fluidi', Annali di Mat. 50 (1960), 379–388.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    E. Hopf, ‘Über die Anfangswertaurgabe für die hydrodynamischen Grundgleichungen', Math. Nachrichten 4 (1951), 213–231.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 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.MathSciNetzbMATHGoogle Scholar
  12. 12.
    C. Kahane, ‘On the spatial analyticity of solutions of the Navier-Stokes equations’ Arch. Rational Mech. Anal. 33 (1969), 386–405.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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.zbMATHGoogle Scholar
  14. 14.
    S. Kaniel and M. Shinbrot, ‘Smoothness of weak solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 24 (1967), 302–324.MathSciNetzbMATHGoogle Scholar
  15. 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.MathSciNetGoogle Scholar
  16. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    M. Lees and M. H. Protter, ‘Unique continuation for parabolic differential equations and inequalities', Duke Math. J. 28 (1961), 369–382.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 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.MathSciNetzbMATHGoogle Scholar
  19. 19.
    J. Leray, ‘Essai sur les mouvements plans d'un liquide visqueux que limitent des parois', J. Math. Pures Appl. 13 (1934), 331–418.zbMATHGoogle Scholar
  20. 20.
    J. Leray, ‘Sur le mouvement d'un liquide visqueux emplissant l'espace', Acta Math. 63 (1934), 193–248.MathSciNetCrossRefGoogle Scholar
  21. 21.
    K. Masuda, ‘On the exponential decay of solutions for some partial differential equations', J. Math. Soc. Japan 19 (1967), 82–90.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    H. Ogawa, ‘Lower bounds for solutions of differential inequalities in Hilbert space', Proc. Amer. Math. Soc. 16 (1965), 1241–1243.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    H. Ogawa, ‘On lower bounds and uniqueness for solutions of the Navier-Stokes equations', J. Math. Mech. 18 (1968), 445–452.MathSciNetzbMATHGoogle Scholar
  25. 25.
    H. Ogawa, ‘On the maximum rate of decay of solutions of parabolic differential inequalities', Arch. Rational Mech. Anal. 38 (1970), 173–177.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    J. Serrin, ‘On the stability of viscous fluid motions', Arch. Rational Mech. Anal. 3 (1959), 1–13.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    J. Serrin, ‘On the interior regularity of weak solutions of the Navier-Stokes equations', Arch. Rational Mech. Anal. 9 (1962), 187–195.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 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

Copyright information

© Springer-Verlag Berlin 1973

Authors and Affiliations

  • R. H. Dyer

There are no affiliations available

Personalised recommendations