带有部分耗散和磁扩散的二维不可压MHD方程组解的正则性条件

摘要

The regularity for the 2D incompressible MHD equations with partial dissipation and magnetic diffusion was studied. A regularity criteria was given for the 2D incompressible MHD equations with partial dissipation and magnetic diffusion (The velocity field and the magnetic field had the partial derivative of two-order type only in the same one direction). It is proved that the uniqueness local classical solution of the 2D incompressible MHD equations with partial dissipation and magnetic diffusion will be global if the partial derivative of magnetic in one direction satisfies one regularity criteria.%研究了带有部分耗散和磁扩散的二维不可压磁流体力学方程组解的正则性问题,给出带有混合部分耗散和磁扩散(速度场和磁场只有同一个方向上的二阶偏导数)的二维不可压Magnetohydrodynamics(MHD)方程组的一个整体正则性条件.证明了只要磁场在一个方向的偏导数满足一定条件,那么带有混合部分耗散和磁扩散的二维不可压MHD方程组的唯一局部经典解为整体经典解.