Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(3): 649-660

Online first article December 17, 2019      Printed May 31, 2020

https://doi.org/10.4134/BKMS.b190402

Copyright © The Korean Mathematical Society.

The 3D Boussinesq equations with regularity in the horizontal component of the velocity

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).