Czechoslovak Mathematical Journal

, Volume 68, Issue 1, pp 219–225 | Cite as

Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component

  • Zujin Zhang


We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of u3 and ω3, which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M.Pokorný (2004).


regularity criterion Navier-Stokes equation 

MSC 2010

35B65 35Q30 76D03 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.College of Mathematics and Computer SciencesGannan Normal UniversityZhanggong, JiangxiP.R. China

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