On a theorem by Sohr for the Navier-Stokes equations

Abstract

In this paper we study some criteria for the full (space-time) regularity of weak solutions to the Navier-Stokes equations. In particular, we generalize some classical and very recent criteria involving the velocity, or its derivatives. More specifically, we show with elementary tools that if a weak solution, or its vorticity, is small in appropriate Marcinkiewicz spaces, then it is regular.

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Correspondence to Luigi C. Berselli or Renato Manfrin.

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Berselli, L.C., Manfrin, R. On a theorem by Sohr for the Navier-Stokes equations. J.evol.equ. 4, 193–211 (2004). https://doi.org/10.1007/s00028-003-1135-2

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Mathematics Subject Classification (2000):

  • Primary 35B65
  • Secondary 35K55, 76D05

Key words:

  • Navier-Stokes equations
  • regularity
  • Marcinkiewicz spaces