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 The 3D Boussinesq equations with regularity in the horizontal component of the velocity Bull. Korean Math. Soc.Published online December 17, 2019 Liu Qiao Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, P.R. of China Abstract : This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., $(\partial_{i}u_{1}; \partial_{j}u_{2}; 0)$ where $i, j\in\{1, 2, 3\}$) in the framework of the anisotropic Lebesgue spaces. More precisely, for \$0