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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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).
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

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