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