Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components

We prove, among others, the following regularity criterion for the solutions to the Navier-Stokes equations: If u is a global weak solution satisfying the energy inequality and ω=∇×u, then u is regular on (0,T), T>0, if two components of ω belong to the space Lq(0,T;B˙∞,∞−3/p) for p∈(3,∞) and 2/q+3/p=2. This result is an improvement of the results presented by Chae and Choe (1999) [7] or Zhang and Chen (2005) [38]. Our method of the proof uses a suitable application of the Bony decomposition and can also be used for the proofs of some other kin criteria. One such example is presented in Appendix.