Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1396-1404.

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Regularity Criteria in Lorentz Spaces for the Three Dimensional Navier-Stokes Equations

Daoguo Zhou()   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan Jiaozuo 454000
  • Received:2020-08-30 Online:2021-10-26 Published:2021-10-08
  • Supported by:
    the NSFC(12071113)


We prove regularity criteria for weak solutions to the three dimensional Navier-Stokes equations, via horizontal part of the velocity, or the vorticity, or the gradient of velocity in scaling invariant Lorentz spaces. Our results improve almost all known regularity criteria involving Lorentz spaces or two components.

Key words: Navier-Stokes equations, Weak solutions, Regularity

CLC Number: 

  • O175