Advertisement

Classical solutions of the Navier-Stokes equations

  • John G. Heywood
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 771)

Keywords

Unbounded Domain Galerkin Approximation Stokes Operator Classical Regularity General Unbounded Domain 
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.
    L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova 31 (1961), 308–340.MathSciNetzbMATHGoogle Scholar
  2. 2.
    C. Foias, Statistical study of the Navier-Stokes equations I, Rend. Sem. Math. Un. Padova 48 (1973), 219–348.MathSciNetzbMATHGoogle Scholar
  3. 3.
    H. Fujita and T. Kato, On the Navier-Stokes initial value problem, I, Arch. Rational Mech. Anal. 16 (1964), 269–315.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    J.G. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, (to appear) Preprint, June 1978.Google Scholar
  5. 5.
    E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr. 4 (1951), 213–231.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    S. Ito, The existence and the uniqueness of regular solution of nonstationary Navier-Stokes equation, J. Fac. Sci. Univ. Tokyo Sect. I A, 9 (1961), 103–140.zbMATHGoogle Scholar
  7. 7.
    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 Ser. Mat. 21 (1957), 655–680.MathSciNetGoogle Scholar
  8. 8.
    O.A. Ladyzhenskaya, On the classicality of generalized solutions of the general nonlinear nonstationary Navier-Stokes equations, Trudy Mat. Inst. Steklov 92 (1966), 100–115.MathSciNetzbMATHGoogle Scholar
  9. 9.
    O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Second Edition, Gordon and Breach, New York, 1969.zbMATHGoogle Scholar
  10. 10.
    K. Masuda, On the stability of incompressible viscous fluid motions past objects, J. Math. Soc. Japan 27 (1975), 294–327.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    G. Prodi, Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzione stazionarie, Rend. Sem. Mat. Univ. Padova 32 (1962), 374–397.MathSciNetzbMATHGoogle Scholar
  12. 12.
    R. Rautmann, Eíne Fehlerschranke für Galerkinapproximationen lokaler Navier-Stokes-Lösungen, in: Int. Schriftenreihe zur num. Math. Bd. 48, Basel 1979.Google Scholar
  13. 13.
    R. Rautmann, On the convergence-rate of nonstationary Navier-Stokes approximations (these proceedings).Google Scholar
  14. 14.
    M. Shinbrot and S. Kaniel, The initial value problem for the Navier-Stokes equations, Arch. Rational Mech. Anal. 21 (1966), 270–285.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    V.A. Solonnikov, Estimates of solutions of nonstationary linearized systems of Navier-Stokes equations, Trudy Mat. Inst. Steklov 70 (1964), 213–317, Amer. Math. Soc. Transl. 75 (1968), 1–116.MathSciNetGoogle Scholar
  16. 16.
    V.A. Solonnikov, On differential properties of the solutions of the first boundary-value problem for nonstationary systems of Navier-Stokes equations, Trudy Mat. Inst. Steklov 73 (1964), 221–291.MathSciNetGoogle Scholar
  17. 17.
    V.A. Solonnikov and V.E. Ščadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov 125 (1973), 196–210; Proc. Seklov Inst. Math. 125 (1973), 186–199.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • John G. Heywood
    • 1
  1. 1.University of British ColumbiaVancouverCanada

Personalised recommendations