Czechoslovak Mathematical Journal, online first, 7 pp.

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.

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

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 2010): 35B65, 35Q30, 76D03

DOI: 10.21136/CMJ.2017.0419-16

Full text available as PDF.


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