Journal of Mathematical Fluid Mechanics

, Volume 1, Issue 4, pp 356–387 | Cite as

On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional Navier—Stokes equations

  • O. A. Ladyzhenskaya
  • G. A. Seregin

Abstract.

We prove a criterion of local Hölder continuity for suitable weak solutions to the Navier—Stokes equations. One of the main part of the proof, based on a blow-up procedure, has quite general nature and can be applied to other problems in spaces of solenoidal vector fields.

Keywords. Navier—Stokes equations, initial-boundary value problems, partial regularity, Hausdorff's dimension. 

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Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • O. A. Ladyzhenskaya
    • 1
  • G. A. Seregin
    • 1
  1. 1.V. A. Steklov Mathematical Institute at St. Petersburg, Fontanka 27, 191011 St. Petersburg, Russia RU

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