Regularity criterion for weak solutions to the 3D Boussinesq equations

Yin-Xia Wang^a,*, Huimin Gao^b

ABSTRACT: In this paper, a regularity criterion for the 3D Boussinesq equations is investigated. We prove that for some T>0 if ∫₀^T|u_z|^β_L^α dt<∞, where 3/α+2/β≤1 and α≥3, then the solution (u,θ) can be extended smoothly beyond t=T. The derivative u_z can be replaced by any directional derivative of u.

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^a	College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
^b	School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

* Corresponding author, E-mail: yinxia117@126.com

Received 18 Feb 2012, Accepted 22 May 2012

Regularity criterion for weak solutions to the 3D Boussinesq equations

Yin-Xia Wanga,*, Huimin Gaob

Yin-Xia Wang^a,*, Huimin Gao^b