Czechoslovak Mathematical Journal, first online, pp. 1-7


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

Zujin Zhang

Received August 7, 2016.   First published October 10, 2017

Abstract:  We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of $u_3$ and $\omega_3$, 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).
Keywords:  regularity criterion; Navier-Stokes equation
Classification MSC:  35B65, 35Q30, 76D03
DOI:  10.21136/CMJ.2017.0419-16

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Affiliations:   Zujin Zhang, College of Mathematics and Computer Sciences, Gannan Normal University, Shangxue Avenue, Ganzhou 341000, Zhanggong, Jiangxi, P. R. China, e-mail: zhangzujin361@163.com

 
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