A regularity criterion of weak solutions to the 3D Boussinesq equations

AIMS Mathematics

关键词: : ;    Regularity criterion;    Boussinesq equations;    a priori estimates;   

DOI  :  10.3934/Math.2017.2.451

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this note, a regularity criterion of weaksolutions to the 3D-Boussinesq equations with respect to Serrin type condition under the framework of Besov space $\overset{.}{B}_{\infty ,\infty}^{r}$. It is shown that the weak solution $(u,\theta )$ is regular on $%(0,T] $ if $u$ satisfies $\int\limits_{0}^{T}{\left\| u\left( \cdot ,t \right) \right\|_{\overset{\cdot R}{\mathop{{{B}_{\infty ,\infty }}}}\,}^{\frac{2}{1+r}}}\ \ dt < \infty ,$ for 0

【 授权许可】

CC BY