In this paper, we are concerned with the uniform estimates of solutions to three dimensional (3D) incompressible magnetic Bénard equations with Navier-slip type boundary conditions being imposed on both velocity and magnetic field in half space, where the physical boundary is assumed to be insulation. Under the assumption that the viscosity and resistivity coefficients are same, which are parameterized by a small parameter of $\epsilon$, the uniform estimates of solutions to the viscous magnetic Bénard system of equations are established in the conormal Sobolev space, which is independent of $\epsilon$. As a direct consequence, the inviscid type limit between the solutions to viscous magnetic Bénard system and the ideal magnetic Bénard system is proved rigorously.

在本文中，我们关注的是对在空间中的速度和磁场都施加了Navier滑移型边界条件的三维（3D）不可压缩磁性Bénard方程解的统一估计。绝缘。在粘度和电阻率系数相同的假设下，通过较小的参数$\epsilon$，在共范式Sobolev空间中建立粘性磁Bénard方程组解的统一估计，该空间与 $\epsilon$。直接的结果是，严格证明了粘性磁贝纳德系统的解与理想磁贝纳德系统的解之间的无粘性类型限制。