Zero Kinematic Viscosity-Magnetic Diffusion Limit of the Incompressible Viscous Magnetohydrodynamic Equations with Navier Boundary Conditions

Abstract

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 W1,∞ (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; W1, p) (2 ≤ p < ∞), and L∞((0, T) × Ω) for some T > 0.