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{ 30\alpha }{ 7\alpha -45}}\left( 0,T;L^{ \alpha ,\infty }\left( \mathbb{ R}^{ 3}\right) \right) \text{ \ \ \ with \ \ }\frac{ 45}{ 7}% \leq \alpha \leq \infty , \label{ eq01} \end{ equation}% and \begin{ equation} j_{ 3}\in L^{ \frac{ 2\beta }{ 2\beta -3}}\left( 0,T;L^{ \beta ,\infty }\left( \mathbb{ R}^{ 3}\right) \right) \text{ \ \ \ with \ \ }\frac{ 3}{ 2}\leq \beta \leq \infty , \label{ eq02} \end{ equation}% which generalize some known results.
Categories: math.AP