A note on regularity criterion for the 3D Boussinesq system with zero thermal conductivity

In this note we prove a regularity criterion u ∈ Ł 2 1 + r ( 0 , T ; B ̇ ∞ , ∞ r ) ( − 1 < r < 1 , r ≠ 0 ) for the 3D Boussinesq system with zero thermal conductivity. Here u is the velocity, B ̇ ∞ , ∞ − r denotes the homogeneous Besov space.