Regularity criterion for weak solutions to the 3D Navier–Stokes equations via two vorticity components in BMO−1. (June 2021) - O, Chol-Jun
Abstract: In this paper, we provide a regularity criterion for 3D Navier–Stokes equations in terms of two vorticity components, which extends a recent result established by Guo, Kučera and Skalák (2018). More precisely, we prove that a unique local strong solution u to 3D Navier–Stokes equations does not blow up at time T provided only two components of vorticity belongs to L 2 ( 0, T ; B M O − 1 ) . We also prove that u can be smoothly extended beyond T, if the horizontal gradient of horizontal components of velocity u belong to L 2 ( 0, T ; B M O − 1 ) . The proof relies on the technique of the Bony decomposition and some Fourier multiplier theorems.