Mathematische Annalen

, Volume 331, Issue 1, pp 87–109 | Cite as

Unbounded normal derivative for the Stokes system near boundary

  • Kyungkeun Kang


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.


Spatial Variable Normal Derivative Local Boundary Stokes System Boundary 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.
    Galdi, G.P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol I. Springer-Verlag, New York, 1994Google Scholar
  2. 2.
    Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 2001Google Scholar
  3. 3.
    Ladyzhenskaya, O.A.: The Mathematical Theory of Viscous Incomprehensible Flow. Second English edition, Gordon and Breach, Science Publishers, New York-London-Paris, 1969Google Scholar
  4. 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, 1968Google Scholar
  5. 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. 6.
    Serrin, J.: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational. Mech. Anal. 9, 187–195 (1962)zbMATHGoogle Scholar
  7. 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)zbMATHGoogle Scholar
  8. 8.
    Teman, R.: Navier-Stokes Equations. Theory and Numerical Analysis. Reprint of the 1984 edition. AMS Chelsea Publishing, Providence, RI, 2001Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kyungkeun Kang
    • 1
  1. 1.University of British ColumbiaVancouverCanada

Personalised recommendations