A note on regularity criterion for the 3D Boussinesq system with partial viscosity

In this note we prove a regularity criterion ω ≔ curl u ∈ L 1 ( 0 , T ; B ̇ ∞ , ∞ 0 ) for the 3D Boussinesq system with partial viscosity. Here u is the velocity, ω is the vorticity and B ̇ ∞ , ∞ 0 denotes the homogeneous Besov space.