This paper devotes to establish an improved regularity criterion for weak solution of 3D incompressible MHD equations. We show that the weak solution is regular, provided that

$$\begin{aligned} \int _{0}^{T}{\frac{\Vert \pi (\cdot ,t)\Vert _{\dot{B}_{\infty ,\infty }^{-1}}^{2}}{\left( e+\ln \left( e+\Vert \pi (\cdot ,t)\Vert _{\dot{B} _{\infty ,\infty }^{-1}}\right) \right) \ln \left( e+\ln \left( e+\Vert \pi (\cdot ,t)\Vert _{\dot{B}_{\infty ,\infty }^{-1}}\right) \right) }}\ dt<\infty . \end{aligned}$$

As a consequence, this improves some previous works.

中文翻译：

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3D MHD方程的弱解的双对数改进正则性准则

本文致力于为3D不可压缩MHD方程的弱解建立改进的正则性准则。我们证明了弱解是规则的，前提是

$$ \ begin {aligned} \ int _ {0} ^ {T} {\ frac {\ Vert \ pi（\ cdot，t）\ Vert _ {\ dot {B} _ {\ infty，\ infty} ^ { -1}} ^ {2}} {\ left（e + \ ln \ left（e + \ Vert \ pi（\ cdot，t）\ Vert _ {\ dot {B} _ {\ infty，\ infty} ^ {- 1}} \ right）\ right）\ ln \ left（e + \ ln \ left（e + \ Vert \ pi（\ cdot，t）\ Vert _ {\ dot {B} _ {\ infty，\ infty} ^ { -1}} \ right）\ right）}} \ dt <\ infty。\ end {aligned} $$

结果，这改善了先前的一些工作。