A regularity criterion for the 3D Boussinesq equations

In this paper, we consider the regularity criteria of 3D incompressible Boussinesq equations. By using the Littlewood–Paley decomposition technique to establishing a regularity criterion in terms of the one-directional derivative of velocity in Besov spaces. Our result improves some previous works (Liu Q. A regularity criterion for the Navier–Stokes equations in terms of one-directional derivative of the velocity. Acta Appl Math. 2015;140(1):1–9; Gala S, Ragusa M A. On the regularity criterion for the Navier–Stokes equations in terms of one-directional derivative. Asian-Eur J Math. 2017;10(1):1750012).