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Local Regularity of Suitable Weak Solutions to the Navier—Stokes Equations Near the Boundary

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Abstract.

We prove a condition of local Hölder continuity for suitable weak solutions to the Navier—Stokes equations near the plane boundary. This condition has the form of the Caffarelli—Kohn—Nirenberg condition for local boundedness of suitable weak solutions at the interior points of the space-time cylinder.

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Authors and Affiliations

  1. V. A. Steklov Institute of Mathematics at Saint Petersburg, Fontanka 27, 191011 St.-Petersburg, Russia, e-mail: seregin@pdmi.ras.ru, , , , , , RU

    G. A. Seregin

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  1. G. A. Seregin
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Accepted: January 31, 2001

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Seregin, G. Local Regularity of Suitable Weak Solutions to the Navier—Stokes Equations Near the Boundary. J. math. fluid mech. 4, 1–29 (2002). https://doi.org/10.1007/s00021-002-8533-z

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  • DOI: https://doi.org/10.1007/s00021-002-8533-z

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