论文标题
3D MHD方程的规律性标准涉及一个速度和一个电流密度分量在Lorentz空间中
A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space
论文作者
论文摘要
在本文中，我们研究了三维（3D）MHD方程的弱解的规律性标准。证明解决方案$（u，b）$是规则的，只要解决方案的一个速度和一个当前密度成分满足％\ begin {equination} u_ {3} \ in l^{\ frac {\ frac {30α} {7α-45}}}}}}}}} \ Mathbb {r}^{3} \ right）\ right）\ text {\ \ \ \ with \ \} l^{\ frac {2β} {2β-3}} \ left（0，t; t; l^{β{β，\ infty} \ left（\ Mathbb {r}^{3} {3} \ right）\ right）\ right）\ right） \ infty，\ label {eq02} \ end {equation}％概括一些已知结果。
In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution $(u,b)$ becomes regular provided that one velocity and one current density component of the solution satisfy% \begin{equation} u_{3}\in L^{\frac{30α}{7α-45}}\left( 0,T;L^{α,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{45}{7}% \leq α\leq \infty , \label{eq01} \end{equation}% and \begin{equation} j_{3}\in L^{\frac{2β}{2β-3}}\left( 0,T;L^{β,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{3}{2}\leq β\leq \infty , \label{eq02} \end{equation}% which generalize some known results.
