Geodesic
Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 219-225.

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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).
DOI : 10.21136/CMJ.2017.0419-16
Classification : 35B65, 35Q30, 76D03
Keywords: regularity criterion; Navier-Stokes equation 
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Zhang, Zujin. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 219-225. doi : 10.21136/CMJ.2017.0419-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0419-16/

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