The 3D Boussinesq equations with regularity in the horizontal component of the velocity
Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 649-660
https://doi.org/10.4134/BKMS.b190402
Published online December 17, 2019
Printed May 31, 2020
Qiao Liu
Hunan Normal University
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
Keywords : Boussinesq equations, regularity criterion, horizontal component, anisotropic Lebesgue spaces
MSC numbers : 35Q355, 35B65, 76D03
Supported by : This work is partially supported by the National Natural Science Foundation of China (11401202).
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