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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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
Mathematics Subject Classification (2000):
- Primary 35B65
- Secondary 35K55, 76D05
- Navier-Stokes equations
- Marcinkiewicz spaces