The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces (Q1771515)

The authors examine the title problem using the technique of Besov and Orlicz spaces. Namely, the authors prove that Leray-Hopf's weak solution of Navier-Stokes equations is unique if the vorticity possesses a sufficient time regularity in logarithmic scale in an Orlicz space, and at the same time possesses a sufficient space regularity in a limiting bounded mean oscillation scale in a Besov space. The proof is based on a generalized critical Sobolev inequality.