Skip to main content
SpringerLink
Log in

Unbounded normal derivative for the Stokes system near boundary

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

Abstract.

We study local boundary regularity for the Stokes system. We show that, unlike in the interior case, non-local effects can lead to a violation of local regularity in the spatial variables near the boundary.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Galdi, G.P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol I. Springer-Verlag, New York, 1994

  2. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 2001

  3. Ladyzhenskaya, O.A.: The Mathematical Theory of Viscous Incomprehensible Flow. Second English edition, Gordon and Breach, Science Publishers, New York-London-Paris, 1969

  4. Ladyzhenskaya, O.A., Solonnikov, V.A., Uralceva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, Amer. Math. Soc. Providence, R.I. 23, 1968

  5. Seregin, G.A.: Some estimates near the boundary for solutions to the non-stationary linearized Navier-Stokes equations. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 271, 204–223 (2000)

    Google Scholar 

  6. Serrin, J.: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational. Mech. Anal. 9, 187–195 (1962)

    MATH  Google Scholar 

  7. Solonnikov, V.A.: Estimates of solutions of nonstationary linearized systems of Navier-Stokes equations. Trudy Mat. Inst. Steklov 70, 213–317 (1964); (In English:A.M.S. Translations, Series II 75, pp. 1–117)

    MATH  Google Scholar 

  8. Teman, R.: Navier-Stokes Equations. Theory and Numerical Analysis. Reprint of the 1984 edition. AMS Chelsea Publishing, Providence, RI, 2001

Download references

Author information

Authors and Affiliations

  1. University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, B.C., Canada, V6T 1Z2

    Kyungkeun Kang

Authors
  1. Kyungkeun Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Mathematics Subject Classification (2000): 35Q30, 76D03, 76D07

Acknowledgement This research was supported in part by NSF Grant No. DMS-9877055. The author express his gratitude to Professor Vladmí r Šverák for helpful discussions. The author also thanks the referees for their valuable comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, K. Unbounded normal derivative for the Stokes system near boundary. Math. Ann. 331, 87–109 (2005). https://doi.org/10.1007/s00208-004-0575-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-004-0575-5

Keywords

Search

Navigation