中文摘要：

为了研究解的正则性,研究了带旋涡的轴对称三维不可压MHD方程组.考虑2类特殊的MHD方程组的光滑弱解：uθ=0、Br=Bz=0和Br=Bz=0,通过采用能量法、Sobolev嵌入法等,证明了如果速度场的径向方向分量ur满足一定条件,则可得到这2类三维不可压的轴对称MHD方程组弱解的正则性.

英文摘要：

To study the regularity criteria of solutions, the three-dimensional axially symmetric incompressible magnetohydrodynamics （ MHD ） equations with swirl are presented. Two types of particular weak solutions to the three-dimensional axially symmetric incompressible MHD equations uθ =0, Br=Bz=0, and Br=Bz=0 are considered. By using the energy method and the embedding method, the regularity criteria for the two types of weak solutions to the three-dimensional axially symmetric incompressible MHD equations are obtained if the radial direction component ur satisfies some conditions.