Mathematische Zeitschrift

, Volume 184, Issue 2, pp 141–149 | Cite as

On optimum regularity of Navier-Stokes solutions at timet=0

  • Reimund Rautmann


Optimum Regularity 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams, R.A.: Sobolev spaces. New York: Academic Press 1975Google Scholar
  2. 2.
    Cattabriga, L.: Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Mat. Sem. Univ. Padova31, 308–340 (1961)Google Scholar
  3. 3.
    Friedmann, A.: Partial differential equations. New York: Holt, Rinehart and Winston 1969Google Scholar
  4. 4.
    Fujita, H., Kato, T.: On the Navier-Stokes initial value problem I. Arch. Rational Mech. Anal.16, 269–315 (1964)Google Scholar
  5. 5.
    Heywood, J.G.: The Navier-Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J.29, 639–681 (1980)Google Scholar
  6. 6.
    Heywood, J.G.: Classical solutions of the Navier-Stokes equations. Proceedings of the IUTAM Symposium (Paderborn 1979), pp. 235–248. Lecture Notes in Math.771. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  7. 7.
    Heywood, J.G., Rannacher, R.: Finite element approximation of the non-stationary Navier-Stokes problem I. Siam J. Numer. Anal.19, 275–311 (1982)Google Scholar
  8. 8.
    Kato, T.: Perturbation theory for linear operators, 2nd ed. Berlin-Heidelberg-New York: Springer 1976Google Scholar
  9. 9.
    Kato, T., Fujita, H.: On the Non-Stationary Navier-Stokes System. Rend. Math. Univ. Padova32, 243–260 (1962)Google Scholar
  10. 10.
    Kielhöfer, H.: Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme. Math. Z.142, 131–160 (1975)Google Scholar
  11. 11.
    Kufner, A., Oldřich, J., Fučik, S.: Function spaces. Leyden: Noordhoff 1977Google Scholar
  12. 12.
    Ladyženskaya, O.A.: The mathematical theory of viscous incompressible flow, 2nd ed. New York: Gordon and Breach 1969Google Scholar
  13. 13.
    Ladyženskaya, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and quasilinear equations of parabolic type. Amer. Math. Soc. Transl. Providence Amer. Math. Soc. 1968Google Scholar
  14. 14.
    Lions, J.L., Magenes, E.: Non-homogeneous boundary value problems and applications, Vol. I. Berlin-Heidelberg-New York: Springer 1972Google Scholar
  15. 15.
    Masuda, K.: On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan27, 294–327 (1975)Google Scholar
  16. 16.
    Rautmann, R.: Eine Fehlerschranke für Galerkinapproximationen lokaler Navier-Stokes-Lösungen. In: Proceedings of a Conference (Oberwolfach 1978), pp. 110–125. Internat. Ser. Numer. Math.48. Basel: Birkhäuser 1979Google Scholar
  17. 17.
    Rautmann, R.: On the convergence-rate of nonstationary Navier-Stokes approximations. Proceedings of the IUTAM Symposium (Paderborn 1979), pp. 425–449. Lecture Notes in Math.771. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  18. 18.
    Rautmann, R.: A semigroup approach to error estimates for nonstationary Navier-Stokes approximations. Methoden Verfahren Math. Physik27, 63–77 (1983)Google Scholar
  19. 19.
    Smale, St.: Smooth solutions of the heat and wave equations. Comment. Math. Helv.55, 1–12 (1980)Google Scholar
  20. 20.
    Solonnikov, V.A.: Estimates of solutions of a nonstationary linearized system of Navier-Stokes equations. Amer. Math. Soc. Transl. (2)75, 1–116 (1968)Google Scholar
  21. 21.
    Temam, R.: Navier-Stokes Equations, rev. ed. Amsterdam: North-Holland 1979Google Scholar
  22. 22.
    Temam, R.: Behaviour at timet=0 of the solutions of semi-linear evolution equations. MRC Technical Summary Report2162, Madison: University of Wisconsin 1980Google Scholar
  23. 23.
    von Wahl, W.: Analytische Abbildungen und semilineare Differentialgleichungen in Banachräumen. Preprint 229, Sonderforschungsbereich 72, Universität Bonn 1978Google Scholar
  24. 24.
    von Wahl, W.: Regularity questions for the Navier-Stokes equations. Proceedings of the IUTAM Symposium (Paderborn 1979), pp. 538–542. Lecture Notes in Math.771, Berlin-Heidelberg-New York: Springer 1980Google Scholar
  25. 25.
    Fujita, H., Morimoto, H.: On fractional powers of the Stokes Operator, Proc. Japan. Acad.46, 1141–1143 (1970)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Reimund Rautmann
    • 1
  1. 1.Fachbereich Mathematik-Informatik der Universität-GesamthochschulePaderbornGermany

Personalised recommendations