Skip to main content
Log in

On the regularity of the pressure of weak solutions of Navier-Stokes equations

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M. E. Bogovski, Solution of the first boundary value problem for the equation of continuity of an incompressible medium. Soviet Math. Dokl.20, 1094–1098 (1979).

    Google Scholar 

  2. L. Caefarelli, R. Kohn andL. Nirenberg, Partial Regularity of Suitable Weak Solutions of the Navier-Stokes Equations. Comm. Pure Appl. Math.35, 771–831 (1982).

    Google Scholar 

  3. W.Erig, Die Gleichungen von Stokes und die Bogovski-Formel. Diplomarbeit, Universität-Gesamthochschule Paderborn 1982.

  4. D. Fujiwara andH. Morimoto, AnL r -Theorem of the Helmholtz-decomposition of vector fields. J. Fac. Sci. Univ. Tokyo24, 685–699 (1977).

    Google Scholar 

  5. Y. Giga, The Stokes operator inL r spaces. Proc. Japan Acad.57, 85–89 (1981).

    Google Scholar 

  6. Y. Giga, Analyticity of the semigroup generated by the Stokes operator inL r spaces. Math. Z.178, 297–329 (1981).

    Google Scholar 

  7. T. Miyakawa, On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J.12, 115–140 (1982).

    Google Scholar 

  8. H. Sohr, Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes. Math. Z.184, 359–375 (1983).

    Google Scholar 

  9. H. Sohr, Optimale lokale Existenzsätze für die Gleichungen von Navier-Stokes. Math. Ann.267, 107–123 (1984).

    Google Scholar 

  10. H. Sohr andW. von Wahl, A New Proof of Leray's Structure Theorem and the Smoothness of Weak Solutions of Navier-Stokes Equations for Large |x|. Bayreuth. Math. Sehr.20, 153–204 (1985).

    Google Scholar 

  11. V. A. Solonnikov, Estimates for Solutions of Nonstationary Navier-Stokes Equations. J. Soviet Math.8, 467–529 (1977).

    Google Scholar 

  12. W. von Wahl, Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen. J. Math. Soc. Japan32, 263–283 (1980).

    Google Scholar 

  13. W. von Wahl, The Equationu′ + A(t)u=fin a Hilbert Space andL p -Estimates for Parabolic Equations. J. London Math. Soc.25, 483–497 (1982).

    Google Scholar 

  14. W. von Wahl, Über das Verhalten fürt→0 der Lösungen nichtlinearer parabolischer Gleichungen, insbesondere der Gleichungen von Navier-Stokes. Bayreuth. Math. Schr.16, 151–277 (1984).

    Google Scholar 

  15. W. von Wahl, Klassische Lösbarkeit im Großen für nichtlineare parabolische Systeme und das Verhalten der Lösungen fürt→∞. Nachr. Akad. Wiss. Göttingen, 5. Akademie der Wissenschaften, Göttingen 1981, 131–177 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sohr, H., von Wahl, W. On the regularity of the pressure of weak solutions of Navier-Stokes equations. Arch. Math 46, 428–439 (1986). https://doi.org/10.1007/BF01210782

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01210782

Keywords

Navigation