Regularity Criterion for the Three-dimensional Boussinesq Equations

We prove that a solution to the three-dimensional Boussinesq equations does not blow-up at time T if $\mathrm{\parallel }{u}_{\le Q}{\mathrm{\parallel }}_{B_{\mathrm{\infty },\mathrm{\infty }}^1}$ is integrable on $(0,T)$, where $u_{\le Q}$ represents the low modes of Littlewood-Paley projection of the velocity $u$.