We investigate a limiting uniqueness criterion in terms of the vorticity for the Navier-Stokes equations in the Besov space. We prove that Leray-Hopf's weak solution is unique under an auxiliary assumption that the vorticity belongs to a scale characterized by the Besov space in space, and the Orlicz space in time direction. As a corollary, we give also the uniqueness criterion in terms of bounded mean oscillation (BMO).
"The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces." Tohoku Math. J. (2) 56 (1) 65 - 77, 2004. https://doi.org/10.2748/tmj/1113246381