manuscripta mathematica

, Volume 69, Issue 1, pp 237–254

On interior regularity criteria for weak solutions of the navier-stokes equations

  • Shuji Takahashi


We are concerned with the behavior of weak solutions of the Navier-Stokes equations near possible singularities. We shall show that if a weak solution is in some Lebesgue space or small in some Lorentz space locally, it does not blowup there. Our basic idea is to estimate integral formulas for vorticity which satisfies parabolic equations.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Shuji Takahashi
    • 1
  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

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