Journal of Mathematical Fluid Mechanics

, Volume 4, Issue 1, pp 1–29

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

  • G. A. Seregin

DOI: 10.1007/s00021-002-8533-z

Cite this article as:
Seregin, G. J. math. fluid mech. (2002) 4: 1. doi:10.1007/s00021-002-8533-z

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.

Keywords. The Navier—Stokes equations, initial-boundary value problems, suitable weak solutions, Hölder continuity. 

Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

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

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