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Interior regularity criteria in weak spaces for the Navier-Stokes equations

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Abstract.

We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω×(0,T), where and 0<T<∞. The local boundedness of a weak solution u is proved under the assumption that is sufficiently small for some (r,s) with and 3≤r<∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Hyunseok Kim & Hideo Kozono

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  1. Hyunseok Kim
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  2. Hideo Kozono
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Correspondence to Hyunseok Kim.

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Mathematics Subject Classification (2000): 35Q30, 76N10

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Kim, H., Kozono, H. Interior regularity criteria in weak spaces for the Navier-Stokes equations. manuscripta math. 115, 85–100 (2004). https://doi.org/10.1007/s00229-004-0484-7

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  • DOI: https://doi.org/10.1007/s00229-004-0484-7

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