A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations

AIMS Mathematics

关键词: : ;    Hall-MHD;    regularity criterion;    Morrey space;    Besov space $\overset {\cdot }{B}_{\infty;    \infty }^{-1}$;   

DOI  :  10.3934/Math.2018.4.565

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this work, we investigate the regularitycriterion for the solution of the Hall-MHD system in three-dimensions. It isproved that if the pressure $\pi $ and the gradient of magnetic field $%\nabla B$ satisfies some kind of space-time integrable condition on $[0,T]$,then the corresponding solution keeps smoothness up to time $T$. This resultimproves some previous works to the Morrey space $\overset{\cdot }{\mathcal{M}}_{2,\frac{3}{r}}$ for $0\leq r<1$ which is larger than $L^{\frac{3}{r}}$.

【 授权许可】

CC BY