We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω ⊂ ℝ³. It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity coefficient. The solution is uniformly bounded in a conormal Sobolev space and W^1,∞ (Ω) which allows us to take the zero kinematic viscosity-magnetic diffusion limit. Moreover, we also get the rates of convergence in L^∞(0, T; L²), L^∞(0, T; W^{1, p}) (2 ≤ p < ∞), and L^∞((0, T) × Ω) for some T > 0.

我们研究了不可压缩粘性磁流体动力学方程的均匀规律性和零运动粘度-磁性扩散极限，其中速度为 Navier 边界条件，光滑有界域 Ω ⊂ ℝ ^{3 中}磁场为完美传导条件。结果表明，不可压缩粘性磁流体动力学方程在有限时间间隔内存在唯一的强解，该方程与粘性系数和磁扩散系数无关。该解在共正交 Sobolev 空间和W ^1,∞ (Ω) 中均匀有界，这允许我们采用零运动粘度-磁扩散极限。此外，我们还得到了L ^∞ (0,; L ² )、L ^∞ (0, T; W ^{1, p} ) (2 ≤ p < ∞ ) 和L ^∞ ((0, T ) × Ω) 对于某些T > 0。