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

In this note we prove a regularity criterion ω≔curlu∈L1(0,T;Ḃ∞,∞0) for the 3D Boussinesq system with partial viscosity. Here uu is the velocity, ωω is the vorticity and Ḃ∞,∞0 denotes the homogeneous Besov space.