Archive for Rational Mechanics and Analysis

, Volume 16, Issue 4, pp 269–315

On the Navier-Stokes initial value problem. I

  • Hiroshi Fujita
  • Tosio Kato
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Cattabriga, L., Su un problema al contorno relativo al sistema di equazioni di Stokes. Rendiconti Seminario Mat. Univ. Padova, 31, 1–33 (1961).Google Scholar
  2. [2]
    Golovkin, K. K., & B. A. Solonnikov, On the first boundary value problem for the non-stationary Navier-Stokes equation. Doklady Akad. Nauk USSR 140, 287–290 (1961).Google Scholar
  3. [3]
    Fujita, H., On the existence and regularity of the steady-state solutions of the Navier-Stokes equation. J. Fac. Sci., Univ. Tokyo, Sec. I 9, 59–102 (1961).Google Scholar
  4. [4]
    Fujita, H., Unique existence of solutions of the Navier-Stokes initial value problem, (an application of fractional powers of operators). Sûgaku (Iwanami) 14, 65–81 (1962).Google Scholar
  5. [5]
    Hopf, E., Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4, 213–231 (1951).Google Scholar
  6. [6]
    Ito, S., The existence and the uniqueness of regular solution of non-stationary Navier-Stokes equation. J. Fac. Sci., Univ. Tokyo, Sec. I 9, 103–140 (1961).Google Scholar
  7. [7]
    Kato, T., Abstract evolution equation of parabolic type in Banach and Hilbert spaces. Nagoya Math. J. 19, 93–125 (1961).Google Scholar
  8. [8]
    Kato, T., Fractional powers of dissipative operators. J. Math. Soc. Japan 13, 246–274 (1961).Google Scholar
  9. [9]
    Kato, T., A generalization of the Heinz inequality. Proc. Japan Acad. 37, 305–308 (1961).Google Scholar
  10. [10]
    Kato, T., & H. Fujita, On the non-stationary Navier-Stokes system. Rendiconti Seminario Math. Univ. Padova 32, 243–260 (1962).Google Scholar
  11. [11]
    Kiselev, A. A., & O. A. Ladyzhenskaia, On existence and uniqueness of the solution of the non-stationary problem for any incompressible viscous fluid. Izv. Akad. Nauk. USSR, 21, 655–680 (1957).Google Scholar
  12. [12]
    Ladyzhenskaia, O. A., Solution “in the large” of the non-stationary boundary value problem for the Navier-Stokes system with two space variables. Comm. Pure Appl. Math. 12, 427–433 (1959).Google Scholar
  13. [13]
    Ladyzhenskaia, O. A., Mathematical Problems for Dynamics of Viscous Incompressible Fluids. Moscow 1961.Google Scholar
  14. [14]
    Leray, J., Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl., Ser. IX 12 1–82 (1933).Google Scholar
  15. [15]
    Leray, J., Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193–248 (1934).Google Scholar
  16. [16]
    Lions, J. L., Sur la régularité et l'unicité des solutions turbulentes des équations de Navier-Stokes. Rendiconti Seminario Mat. Univ. Padova 30, 16–23 (1960).Google Scholar
  17. [17]
    Lions, J. L., Sur les espaces d'interpolation; dualité. Math. Scand. 9, 147–177 (1961).Google Scholar
  18. [18]
    Lions, J. L., & G. Prodi, Un théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2. C.R. Acad. Sci. Paris 248, 3519–3521 (1959).Google Scholar
  19. [19]
    Odqvist, F. K. G., Über die Randwertaufgabe der Hydrodynamik zäher Flüssigkeiten. Math. Z. 32, 329–375 (1930).Google Scholar
  20. [20]
    Ohyama, T., Interior regularity of weak solutions of the time-dependent Navier Stokes equation. Proc. Japan Acad. 36, 273–277 (1960).Google Scholar
  21. [21]
    Oseen, C. W., Hydrodynamik. Leipzig 1927.Google Scholar
  22. [22]
    Serrin, J., On the interior regularity of weak solutions of the Navier-Stokes equation. Arch. Rational Mech. Anal. 9, 187–195 (1962).Google Scholar
  23. [23]
    Sobolevskii, P. E., On non-stationary equations of hydrodynamics for viscous fluid. Doklady Akad. Nauk USSR 128, 45–18 (1959).Google Scholar
  24. [24]
    Sobolevskii, P. E., On the smoothness of generalized solutions of the Navier-Stokes equation, ibid Nauk USSR 131, 758–760 (1960).Google Scholar

Copyright information

© Springer-Verlag 1964

Authors and Affiliations

  • Hiroshi Fujita
    • 1
    • 2
  • Tosio Kato
    • 1
    • 2
  1. 1.Department of MathematicsStanford UniversityUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeley

Personalised recommendations