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This note is devoted to the study of the regularity of strong solutions to the Boussinesq system in which the vorticity and to improve a result of Fan and Ozawa [J. Fan, T. Ozawa, Regularity conditions for the 3D Boussinesq equations with partial viscosity terms, Nonlinearity 22 (2009), pp. 553–568] and Gala [S. Gala, Remark on the regularity criterion on strong solutions to the 3D Boussinesq equations (Submitted)].
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