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

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Abstract

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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  1. Department of Mathematics, Hokkaido University, 060, Sapporo, Japan

    Shuji Takahashi

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  1. Shuji Takahashi
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Takahashi, S. On interior regularity criteria for weak solutions of the navier-stokes equations. Manuscripta Math 69, 237–254 (1990). https://doi.org/10.1007/BF02567922

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  • DOI: https://doi.org/10.1007/BF02567922

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